A Bibliography of the Novikov Conjecture

Steven C. Ferry, Andrew Ranicki, and Jonathan Rosenberg

last updated June, 1996

S. C. Ferry was partially supported by NSF Grant # DMS-93-05758. J. Rosenberg was partially supported by NSF Grant # DMS-92-25063.

A Bibliography of the Novikov Conjecture 1

References

[Ad] A. Adem, Characters and K-theory of discrete groups, Invent. Math. 114 (1993), 489–514.

[AnCFK] D. R. Anderson, F. X. Connolly, S. C. Ferry, and E. K. Pedersen, Algebraic K-theory with continuous control at infinity, J. Pure Appl. Alg. 94 (1994), 25–48.

[AnM1] D. R. Anderson and H. J. Munkholm, Boundedly Controlled Topology, Lect. Notes in Math., vol. 1323, Springer-Verlag, Berlin, Heidelberg, New York, 1988.

[AnM2] D. R. Anderson and H. J. Munkholm, Geometric modules and algebraic K-ho-mology theory, K-Theory 3 (1990), 561–602.

[Ang] N. Anghel, On the index of Callias-type operators, Geom. and Funct. Anal. 3 (1993), 431–438.

[At1] M. Atiyah, Characters and cohomology of finite groups, Publ. Math. Inst. Hautes Études Sci. 9 (1961), 23–64.

[At2] M. Atiyah, Elliptic operators, discrete groups and von Neumann algebras, Colloque analyse et topologie en l’honneur de Henri Cartan, Astérisque, vol. 32–33, Soc. Math. de France, Paris, 1976, pp. 43–72.

[Att1] O. Attie, Quasi-isometry classification of some manifolds of bounded geometry, Math. Z. 216 (1994), 501–527.

[Att2] O. Attie, A surgery theory for manifolds of bounded geometry, preprint, Mc-Master Univ. (1994).

[AtBW] O. Attie, J. Block, and S. Weinberger, Characteristic classes and distortion of diffeomorphisms, J. Amer. Math. Soc. 5 (1992), 919–921.

[AsV] A. H. Assadi and P. Vogel, Semifree finite group actions on compact manifolds, Algebraic and geometric topology (New Brunswick, NJ, 1983), Lect. Notes in Math., vol. 1126, Springer-Verlag, Berlin, Heidelberg, New York, 1985, pp. 1–21.

[Bass] H. Bass, Algebraic K-Theory, W. A. Benjamin, New York and Amsterdam, 1968.

[BHS] H. Bass, A. Heller and R. Swan, The Whitehead group of a polynomial extension, Publ. Math. Inst. Hautes Études Sci. 22 (1964), 61–79.

[BC1] P. Baum and A. Connes, Geometric K-theory for Lie groups and foliations, Preprint, Inst. Hautes Études Sci., 1982.

[BC2] P. Baum and A. Connes, Leafwise homotopy equivalence and rational Pontrjagin classes, Foliations: Proceedings, Tokyo, 1983 (I. Tamura, ed.), Advanced Studies in Pure Math., vol. 5, Kinokuniya and North-Holland, Tokyo, Amsterdam, 1985, pp. 1–14.

[BC3] P. Baum and A. Connes, Chern character for for discrete groups, A fête of topology, Academic Press, Boston, 1988, pp. 163–232.

[BC4] P. Baum and A. Connes, K-theory for discrete groups, Operator algebras and applications, Vol. 1 (D. Evans and M. Takesaki, eds.), London Math. Soc. Lecture Note Ser., vol. 135, Cambridge Univ. Press, Cambridge, 1988, pp. 1–20.

2 Steven C. Ferry, Andrew Ranicki, and Jonathan Rosenberg

[BCH] P. Baum, A. Connes, and N. Higson, Classifying space for proper actions and K-theory of group C^{∗}-algebras, C^{∗}-algebras: 1943–1993, A Fifty-Year Celebration (R. S. Doran, ed.), Contemp. Math., vol. 167, Amer. Math. Soc., Providence, RI, 1994, pp. 241–291.

[BHP] P. Baum, N. Higson, and R. Plymen, Equivariant homology for SL(2) of a p-adic field, Index Theory and Operator Algebras (J. Fox and P. Haskell, eds.), Contemp. Math., vol. 148, Amer. Math. Soc., Providence, RI, 1993, pp. 1–18.

[BeM] S. Bentzen and I. Madsen, Trace maps in algebraic K-theory and the Coates-Wiles homomorphism, J. reine angew. Math. 411 (1990), 171–195.

[Bi] R. Bieri, A group with torsion-free 2-divisible homology and Cappell’s result on the Novikov Conjecture, Invent. Math. 33 (1976), 181–184.

[Black] B. Blackadar, K-Theory for Operator Algebras, Math. Sciences Research Inst. Publications, vol. 5, Springer-Verlag, New York, Berlin, Heidelberg, London, Paris, Tokyo, 1986.

[BlocW] J. Block and S. Weinberger, Aperiodic tilings, positive scalar curvature and amenability of spaces, J. Amer. Math. Soc. 5 (1992), 907–918.

[BöHM1] M. Bökstedt, W. C. Hsiang, and I. Madsen, The cyclotomic trace and the K-theoretic analogue of Novikov’s conjecture, Proc. Nat. Acad. Sci. U.S.A. 86 (1989), 8607–8609.

[BöHM2] M. Bökstedt, W. C. Hsiang, and I. Madsen, The cyclotomic trace and algebraic

K-theory of spaces, Invent. Math. 111 (1993), 465–539.

[Br1] W. Browder, Homotopy type of differentiable manifolds, Proc. Århus Topology Symp., unpublished mimeographed notes, 1962; reprinted, Novikov Conjectures, Index Theorems and Rigidity, vol. 1 (S. Ferry, A. Ranicki, and J. Rosenberg, eds.), London Math. Soc. Lecture Notes, vol. 226, Cambridge Univ. Press, Cambridge, 1995, pp. 97–100.

[Br2] W. Browder, Structures on M ×ℝ, Proc. Camb. Phil. Soc. 61 (1965), 337–345.

[Br3] W. Browder, Manifolds with π_{1} = ℤ, Bull. Amer. Math. Soc. 72 (1966), 238–244.

[Br4] W. Browder, Surgery on Simply-Connected Manifolds, Ergebnisse der Math. und ihrer Grenzgebiete, vol. 65, 1972.

[BrHs] W. Browder and W. C. Hsiang, G-actions and the fundamental group, Invent. Math. 65 (1982), 411–424.

[BryF] J. Bryant, S. Ferry, W. Mio, and S. Weinberger, Topology of homology manifolds, Bull. Amer. Math. Soc. 28 (1993), 324–328.

[BryP] J. L. Bryant and M. E. Petty, Splitting manifolds as M × ℝ where M has a k-fold end structure, Topology Appl. 14 (1982), 87–104.

[Bur] D. Burghelea, The cyclic cohomology of group rings, Comment. Math. Helv. 60 (1985), 354–365.

[Cap1] S. E. Cappell, A splitting theorem for manifolds and surgery groups, Bull. Amer. Math. Soc. 77 (1971), 281–286.

[Cap2] S. E. Cappell, A splitting theorem for manifolds, Invent. Math. 33 (1976), 69–170.

[Cap3] S. E. Cappell, On homotopy invariance of higher signatures, Invent. Math. 33 (1976), 171–179.

[CaSW] S. E. Cappell, J. L. Shaneson, and S. Weinberger, Classes topologiques caractéristiques pour les actions de groupes sur les espaces singuliers, C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), 293–295.

[CaW1] S. E. Cappell and S. Weinberger, A geometric interpretation of Siebenmann’s periodicity phenomenon, Geometry and topology (Athens, Ga. 1985), Lecture Notes in Pure and Appl. Math., vol. 105, Dekker, New York, NY, 1987, pp. 47–52.

[CaW2] S. E. Cappell and S. Weinberger, Classification de certains espaces stratifiés, C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), 399–401.

[Car1] G. Carlsson, Equivariant stable homotopy and Segal’s Burnside ring conjecture, Ann. of Math. 120 (1984), 189–224.

[Car2] G. Carlsson, Segal’s Burnside ring conjecture and the homotopy limit problem, Homotopy Theory (E. Rees and J. D. S. Jones, eds.), London Math. Soc. Lect. Notes, vol. 117, Cambridge Univ. Press, Cambridge, 1987, pp. 6–34.

[Car3] G. Carlsson, Homotopy fixed points in the algebraic K-theory of certain infinite discrete groups, Advances in Homotopy Theory (S. Salamon, B. Steer, and W. Sutherland, eds.), London Math. Soc. Lect. Notes, vol. 139, Cambridge Univ. Press, Cambridge, 1990, pp. 5–10.

[Car4] G. Carlsson, Proper homotopy theory and transfers for infinite groups, Algebraic Topology and its Applications (G. Carlsson, R. Cohen, W.-C. Hsiang, and J. D. S. Jones, eds.), M. S. R. I. Publications, vol. 27, Springer-Verlag, New York, 1994, pp. 1–14.

[Car5] G. Carlsson, Bounded K-theory and the assembly map in algebraic K-theory, Novikov Conjectures, Index Theorems and Rigidity, vol. 2 (S. Ferry, A. Ranicki, and J. Rosenberg, eds.), London Math. Soc. Lecture Notes, vol. 227, Cambridge Univ. Press, Cambridge, 1995, pp. 5–127.

[CarP1] G. Carlsson and E. K. Pedersen, Controlled algebra and the Novikov conjectures for K- and L-theory, Topology 34 (1995), 731–758.

[CarP2] G. Carlsson and E. K. Pedersen, Čech homology and the Novikov conjecture in K- and L-theory, Preprint, SUNY at Binghamton, 1995.

[CarPV] G. Carlsson, E. K. Pedersen, and W. Vogell, Continuously controlled algebraic K-theory of spaces and the Novikov conjecture, Preprint, SUNY at Binghamton, 1993.

[Carter] D. W. Carter, Localization in lower algebraic K-theory, Comm. Algebra 8 (1980), 603–622; Lower K-theory of finite groups, Comm. Algebra 8 (1980), 1927–1937.

[ChapF] T. A. Chapman and S. C. Ferry, Approximating homotopy equivalences by homeomorphisms, Amer. J. Math. 101 (1979), 583–607.

[ChG] J. Cheeger and M. Gromov, Bounds on the von Neumann dimension of L^{2}-co-homology and the Gauss-Bonnet theorem for open manifolds, J. Diff. Geom. 21 (1985), 1–34.

[ChG] J. Cheeger and M. Gromov, L^{2}-cohomology and group cohomology, Topology 25 (1986), 189–215.

[CoJ] R. L. Cohen and J. D. S. Jones, Algebraic K-theory of spaces and the Novikov conjecture, Topology 29 (1990), 317–344.

[Con1] A. Connes, A survey of foliations and operator algebras, Operator Algebras and Applications (Kingston, Ont., 1980) (R. V. Kadison, ed.), Proc. Symp. Pure Math., vol. 38, Part 1, Amer. Math. Soc., Providence, 1982, pp. 521–628.

[Con2] A. Connes, Cyclic cohomology and the transverse fundamental class of a foliation, Geometric methods in operator algebras (Kyoto, 1983) (H. Araki and E. G. Effros, eds.), Pitman Res. Notes Math., vol. 123, Longman Sci. Tech., Harlow, 1986, pp. 52–144.

[Con3] A. Connes, Introduction to noncommutative differential geometry, Arbeitstagung Bonn 1984, Lecture Notes in Math., vol. 1111, Springer-Verlag, Berlin, Heidelberg, New York, 1985, pp. 3–16.

[Con4] A. Connes, Cyclic cohomology and noncommutative differential geometry, Proc. International Congress of Mathematicians (Berkeley, Calif., 1986), vol. 1, Amer. Math. Soc., Providence, RI, 1987, pp. 879–889.

[Con5] A. Connes, Cyclic cohomology and noncommutative differential geometry, Géometrie différentielle (Paris, 1986), Travaux en Cours, vol. 33, Hermann, Paris, 1988, pp. 33–50.

[Con6] A. Connes, Géometrie non commutative, InterEditions, Paris, 1990.

[Con7] A. Connes, Noncommutative Geometry, Academic Press, San Diego, 1994.

[CGM1] A. Connes, M. Gromov, and H. Moscovici, Conjecture de Novikov et fibrés presques plats, C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), 273–277.

[CGM2] A. Connes, M. Gromov, and H. Moscovici, Group cohomology with Lipschitz control and higher signatures, Geom. Funct. Anal. 3 (1993), 1–78.

[CM1] A. Connes and H. Moscovici, Conjecture de Novikov et groupes hyperboliques, C. R. Acad. Sci. Paris Sér. I Math. 307 (1988), 475–480.

[CM2] A. Connes and H. Moscovici, Cyclic cohomology, the Novikov conjecture and hyperbolic groups, Topology 29 (1990), 345–388.

[CS] A. Connes and G. Skandalis, The longitudinal index theorem for foliations, Publ. Res. Inst. Math. Sci. (Kyoto Univ.) 20 (1984), 1139–1183.

[CST] A. Connes, D. Sullivan and N. Teleman, Quasiconformal mappings, operators on Hilbert space, and local formulæ for characteristic classes, Topology 33 (1994), 663–681.

[CyK1] F. X. Connolly and T. Koźniewski, Finiteness properties of classifying spaces of proper Γ-actions, J. Pure Applied Algebra 41 (1986), 17–36.

[CyK2] F. X. Connolly and T. Koźniewski, Rigidity and crystallographic groups, I, Invent. Math. 99 (1990), 25–48.

[CyK3] F. X. Connolly and T. Koźniewski, Examples of lack of rigidity in crystallographic groups, Algebraic Topology, Poznań 1989 (S. Jackowski, B. Oliver, and K. Pawałowski, eds.), Lecture Notes in Math., vol. 1474, Springer-Verlag, Berlin, Heidelberg, and New York, 1991, pp. 139–145.

[Cu1] J. Cuntz, The K-groups for free products of C^{∗}-algebras, Operator Algebras and Applications (Kingston, Ont, 1980) (R. V. Kadison, ed.), Proc. Symp. Pure Math., vol. 38, Part 1, Amer. Math. Soc., Providence, 1982, pp. 81–84.

[Cu2] J. Cuntz, K-theory for certain C^{∗}-algebras, II, J. Operator Theory 5 (1981), 101–108.

[DaL] J. F. Davis and W. Lück, Spaces over a category and assembly maps in isomorphism conjectures in K- and L-theory, Preprint, Univ. of Mainz, 1996.

[Dav] M. W. Davis, Coxeter groups and aspherical manifolds, Algebraic topology, Aarhus 1982, Lecture Notes in Math., vol. 1051, Springer-Verlag, Berlin, Heidelberg, New York, 1984, pp. 197–221.

[Di] Do Ngoc Diep, C^{∗}-complexes de Fredholm, I, Acta Math. Vietnam. 9 (1984), 121–130; II, ibid. 9 (1984), 193–199.

[Do] R. G. Douglas, C^{∗}-algebra extensions and K-homology, Ann. of Math. Studies, vol. 95, Princeton University Press, Princeton, NJ, 1980.

[DrFW] A. N. Dranishnikov, S. Ferry, and S. Weinberger, A large Riemannian manifold which is flexible, preprint, SUNY at Binghamton.

[Fack1] T. Fack, K-théorie bivariante de Kasparov, Séminaire Bourbaki, 1982–83, exposé no. 605, Astérisque 105–106 (1983), 149–166.

[Fack2] T. Fack, Sur la conjecture de Novikov, Index theory of elliptic operators, foliations, and operator algebras (J. Kaminker, K. C. Millett and C. Schochet, eds.), Contemp. Math., vol. 70, Amer. Math. Soc., Providence, RI, 1988, pp. 43–102.

[FarL] M. S. Farber and J. P. Levine, Jumps of the eta-invariant, with an appendix by S. Weinberger, preprint, Brandeis Univ., 1994.

[Far] F. T. Farrell, The obstruction to fibering a manifold over a circle, Indiana Univ. Math. J. 21 (1971), 315–346.

[FarHs1] F. T. Farrell and W. C. Hsiang, A geometric interpretation of the Künneth formula for algebraic K-theory, Bull. Amer. Math. Soc. 74 (1968), 548–553.

[FarHs2] F. T. Farrell and W.-C. Hsiang, A formula for K_{1}R_{α}[T], Applications of Categorical Algebra (New York, 1968), Proc. Symp. Pure Math., vol. 17, Amer. Math. Soc., Providence, 1970, pp. 192–218.

[FarHs3] F. T. Farrell and W.-C. Hsiang, Manifolds with π_{1} = G ×_{α} T, Amer J. Math. 95 (1973), 813–848.

[FarHs4] F. T. Farrell and W.-C. Hsiang, Rational L-groups of Bieberbach groups, Comment. Math. Helv. 52 (1977), 89–109.

[FarHs5] F. T. Farrell and W.-C. Hsiang, On the rational homotopy groups of the diffeomorphism groups of discs, spheres and aspherical manifolds, Algebraic and geometric topology, Proc. Sympos. Pure Math., vol. 32 (Part 1), Amer. Math. Soc., Providence, RI, 1978, pp. 325–337.

[FarHs6] F. T. Farrell and W.-C. Hsiang, Remarks on Novikov’s conjecture and the topological-Euclidean space form problem, Algebraic topology, Aarhus 1978, Lecture Notes in Math., vol. 763, Springer-Verlag, Berlin, Heidelberg, New York, 1979, pp. 635–642.

[FarHs7] F. T. Farrell and W.-C. Hsiang, The topological-Euclidean space form problem, Invent. Math. 45 (1978), 181–192.

[FarHs8] F. T. Farrell and W.-C. Hsiang, On Novikov’s conjecture for nonpositively curved manifolds, I, Ann. of Math. 113 (1981), 199–209.

[FarHs9] F. T. Farrell and W.-C. Hsiang, The Whitehead group of poly-(finite or cyclic) groups, J. London Math. Soc. 24 (1981), 308–324.

[FarHs10] F. T. Farrell and W.-C. Hsiang, The stable topological-hyperbolic space form problems for complete manifolds of finite volume, Invent. Math. 69 (1982), 155–170.

[FarHs11] F. T. Farrell and W.-C. Hsiang, Topological characterization of flat and almost flat Riemannian manifolds M^{n} (n ≠ 3, 4), Amer. J. Math. 105 (1983), 641–672.

[FarHs12] F. T. Farrell and W.-C. Hsiang, On Novikov’s conjecture for cocompact discrete subgroups of a Lie group, Algebraic topology, Aarhus 1982, Lecture Notes in Math., vol. 1051, Springer-Verlag, Berlin, Heidelberg, New York, 1984, pp. 38–48.

[FJ1] F. T. Farrell and L. E. Jones, Implications of the geometrization conjecture for the algebraic K-theory of 3-manifolds, Geometry and topology (Athens, GA, 1985), Lect. Notes in Pure and Appl. Math., vol. 105, Marcel Dekker, New York, 1987, pp. 109–113.

[FJ2] F. T. Farrell and L. E. Jones, h-cobordisms with foliated control, Bull. Amer. Math. Soc. 15 (1986), 69–72; Erratum, ibid. 16 (1987), 177.

[FJ3] F. T. Farrell and L. E. Jones, K-theory and dynamics, I, Ann. of Math. 124 (1986), 531–569; II, ibid. 126 (1987), 451–493.

[FJ4] F. T. Farrell and L. E. Jones, Topological rigidity for hyperbolic manifolds, Bull. Amer. Math. Soc. 19 (1988), 277–282.

[FJ5] F. T. Farrell and L. E. Jones, A topological analogue of Mostow’s rigidity theorem, J. Amer. Math. Soc. 2 (1989), 257–370.

[FJ6] F. T. Farrell and L. E. Jones, Rigidity and other topological aspects of compact nonpositively curved manifolds, Bull. Amer. Math. Soc. 22 (1990), 59–64.

[FJ7] F. T. Farrell and L. E. Jones, Classical Aspherical Manifolds, Conf. Board of the Math. Sciences Regional Conf. Ser. in Math., vol. 75, Amer. Math. Soc., Providence, RI, 1990.

[FJ8] F. T. Farrell and L. E. Jones, Rigidity in geometry and topology, Proc. International Congress of Mathematicians (Kyoto, 1990), vol. 1, Math. Soc. Japan, Tokyo, 1991, pp. 653–663.

[FJ9] F. T. Farrell and L. E. Jones, Computations of stable pseudoisotopy spaces for aspherical manifolds, Algebraic Topology, Poznań 1989 (S. Jackowski, B. Oliver, and K. Pawałowski, eds.), Lecture Notes in Math., vol. 1474, Springer-Verlag, Berlin, Heidelberg, and New York, 1991, pp. 59–74.

[FJ10] F. T. Farrell and L. E. Jones, Stable pseudoisotopy spaces of compact non-posi-tively curved manifolds, J. Diff. Geom. 34 (1991), 769–834.

[FJ11] F. T. Farrell and L. E. Jones, Foliated control without radius of injectivity restrictions, Topology 30 (1991), 117–142.

[FJ12] F. T. Farrell and L. E. Jones, Isomorphism conjectures in algebraic K-theory, J. Amer. Math. Soc. 6 (1993), 249–297.

[FJ13] F. T. Farrell and L. E. Jones, Topological rigidity for compact nonpositively curved manifolds, Differential Geometry (Los Angeles, 1990) (R. E. Greene and S.-T. Yau, eds.), Proc. Symp. Pure Math., vol. 54, Part 3, Amer. Math. Soc., Providence, 1993, pp. 229–274.

[Fer1] S. C. Ferry, Homotoping ϵ-maps to homeomorphisms, Amer. J. Math 101

(1979), 567–582.

[Fer2] S. Ferry, Remarks on Steenrod homology, Novikov Conjectures, Index Theorems and Rigidity, vol. 2 (S. Ferry, A. Ranicki, and J. Rosenberg, eds.), London Math. Soc. Lecture Notes, vol. 227, Cambridge Univ. Press, Cambridge, 1995, pp. 148–166.

[FHP] S. Ferry, I. Hambleton and E. K. Pedersen, A survey of bounded surgery theory and applications, Algebraic Topology and its Applications (G. E. Carlsson, R. L. Cohen, W.-c. Hsiang, and J. D. S. Jones, eds.), Math. Sci. Res. Inst. Publ., vol. 27, Springer-Verlag, New York, Berlin, 1994, pp. 57–80.

[FP] S. Ferry and E. K. Pedersen, Epsilon surgery theory, Novikov Conjectures, Index Theorems and Rigidity, vol. 2 (S. Ferry, A. Ranicki, and J. Rosenberg, eds.), London Math. Soc. Lecture Notes, vol. 227, Cambridge Univ. Press, Cambridge, 1995, pp. 167–226.

[FRR] S. Ferry, A. Ranicki, and J. Rosenberg, A history and survey of the Novikov Conjecture, Novikov Conjectures, Index Theorems and Rigidity, vol. 1 (S. Ferry, A. Ranicki, and J. Rosenberg, eds.), London Math. Soc. Lecture Notes, vol. 226, Cambridge Univ. Press, Cambridge, 1995, pp. 7–66.

[FRW] S. Ferry, J. Rosenberg, and S. Weinberger, Phénomènes de rigidité topologique équivariante, C. R. Acad. Sci. Paris Sér. I Math. 306 (1988), 777–782.

[FW1] S. Ferry and S. Weinberger, Curvature, tangentiality, and controlled topology, Invent. Math. 105 (1991), 401–414.

[FW2] S. Ferry and S. Weinberger, A coarse approach to the Novikov Conjecture, Novikov Conjectures, Index Theorems and Rigidity, vol. 1 (S. Ferry, A. Ranicki, and J. Rosenberg, eds.), London Math. Soc. Lecture Notes, vol. 226, Cambridge Univ. Press, Cambridge, 1995, pp. 147–163.

[FH] J. Fox and P. Haskell, K-theory and the spectrum of discrete subgroups of Spin(4, 1), Operator Algebras and Topology (Craiova, 1989), Pitman Res. Notes Math., vol. 270, Longman Sci. Tech., Harlow, 1992, pp. 30–44.

[GM] I. M. Gelfand and A. S. Mishchenko, Quadratic forms over commutative group rings, and K-theory, Funkc. Anal i Priložen. 3 no. 4 (1969), 28–33; English translation, Funct. Anal. and its Appl. 3 (1969), 277–281.

[Gong] D. Gong, Equivariant Novikov Conjecture for groups acting on Euclidean buildings, preprint, Univ. of Chicago.

[GonL] D. Gong and K. Liu, On the rigidity of higher elliptic genera, preprint, Univ. of Chicago.

[Gor] V. V. Gorbatsevich, On some cohomology invariants of compact homogeneous manifolds, Lie groups, their discrete subgroups, and invariant theory, Adv. Soviet Math., vol. 8, Amer. Math. Soc., Providence, RI, 1992, pp. 69–85.

[Gr1] M. Gromov, Large Riemannian manifolds, Curvature and Topology of Riemannian Manifolds, Proc., Katata, 1985 (K. Shiohama, T. Sakai and T. Sunada, eds.), Lecture Notes in Math., vol. 1201, 1986, pp. 108–121.

[Gr2] M. Gromov, Hyperbolic groups, Essays in Group Theory (S. M. Gersten, ed.), Math. Sciences Research Inst. Publications, vol. 8, Springer-Verlag, New York, Berlin, Heidelberg, London, Paris, Tokyo, 1987, pp. 75–263.

[Gr3] M. Gromov, Kähler hyperbolicity and L_{2}-Hodge theory, J. Diff. Geometry 33

(1991), 263–292.

[Gr4] M. Gromov, Asymptotic invariants for infinite groups, Geometric Group Theory (G. A. Niblo and M. A. Roller, eds.), London Math. Soc. Lect. Notes, vol. 182, Cambridge Univ. Press, Cambridge, 1993, pp. 1–295.

[Gr5] M. Gromov, Geometric reflections on the Novikov Conjecture, Novikov Conjectures, Index Theorems and Rigidity, vol. 1 (S. Ferry, A. Ranicki, and J. Rosenberg, eds.), London Math. Soc. Lecture Notes, vol. 226, Cambridge Univ. Press, Cambridge, 1995, pp. 164–173.

[Gr6] M. Gromov, Positive curvature, macroscopic dimension, spectral gaps and higher signatures, Functional Analysis on the Eve of the 21st Century (Proc. conf. in honor of I. M. Gelfand’s 80th birthday), vol. 2 (S. Gindikin, J. Lepowsky and R. Wilson, eds.), Progress in Math., vol. 132, Birkhäuser, Boston, 1996, pp. 1–213.

[GL1] M. Gromov and H. B. Lawson, Jr., Spin and scalar curvature in the presence of a fundamental group. I, Ann. of Math. 111 (1980), 209–230.

[GL2] M. Gromov and H. B. Lawson, Jr., Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Publ. Math. Inst. Hautes Études Sci. 58 (1983), 83–196.

[HaMTW] I. Hambleton, J. Milgram, L. Taylor and B. Williams, Surgery with finite fundamental group, Proc. London Math. Soc. 56 (1988), 349–379.

[Has] P. Haskell, Direct limits in an equivariant K-theory defined by proper cocycles, Michigan Math. J. 36 (1989), 17–27.

[Hi] G. Higman, Units in group rings, Proc. Lond. Math. Soc. (2) 46 (1940), 231–248.

[Hig1] N. Higson, A primer on KK-theory, Operator theory: operator algebras and applications (Durham, NH, 1988), Proc. Sympos. Pure Math., vol. 51, Part 1, Amer. Math. Soc., Providence, RI, 1990, pp. 239–283.

[Hig2] N. Higson, On the relative K-homology theory of Baum and Douglas, Unpublished preprint, 1990.

[Hig3] N. Higson, On the cobordism invariance of the index, Topology 30 (1991), 439–443.

[HigPR] N. Higson, E. K. Pedersen, and J. Roe, C^{∗}-algebras and controlled topology, preprint, 1995.

[HigR1] N. Higson and J. Roe, A homotopy invariance theorem in coarse cohomology and K-theory, Trans. Amer. Math. Soc. 345 (1994), 347–365.

[HigR2] N. Higson and J. Roe, On the coarse Baum-Connes conjecture, Novikov Conjectures, Index Theorems and Rigidity, vol. 2 (S. Ferry, A. Ranicki, and J. Rosenberg, eds.), London Math. Soc. Lecture Notes, vol. 227, Cambridge Univ. Press, Cambridge, 1995, pp. 227–254.

[HigRY] N. Higson, J. Roe, and G. Yu, A coarse Mayer-Vietoris principle, Math. Proc. Camb. Philos. Soc. 114 (1993), 85–97.

[Hil] M. Hilsum, Fonctorialité en K-théorie bivariante pour les variétés lipschitziennes, K-Theory 3 (1989), 401–440.

[HilS] M. Hilsum and G. Skandalis, Invariance par homotopie de la signature à coef-

ficients dans un fibré presque plat, J. reine angew. Math. 423 (1992), 73–99.

[Hir] F. Hirzebruch, The signature theorem: reminiscences and recreation, Prospects in mathematics (Proc. Sympos., Princeton Univ., Princeton, N.J., 1970), Ann. of Math. Studies, vol. 70, Princeton Univ. Press, Princeton, NJ, 1971, pp. 3–31.

[Ho] J. G. Hollingsworth, A short list of problems, Geometric topology (Proc. Georgia Topology Conf., Athens, Ga., 1977), Academic Press, New York and London, 1979, pp. 685–692.

[Hs1] W.-C. Hsiang, On π_{i} Diff M^{n}, Geometric topology (Proc. Georgia Topology Conf., Athens, Ga., 1977), Academic Press, New York and London, 1979, pp. 351–365.

[Hs2] W.-C. Hsiang, Geometric applications of algebraic K-theory, Proc. International Congress of Mathematicians (Warsaw, 1983), Polish Scientific Publishers, Warsaw, 1984, pp. 99–119.

[Hs3] W.-C. Hsiang, Borel’s conjecture, Novikov’s conjecture and the K-theoretic analogues, Algebra, analysis and geometry (Taipei, 1988), World Sci. Publishing, Teaneck, NJ, 1989, pp. 39–58.

[HsR] W.-C. Hsiang and H. D. Rees, Mishchenko’s work on Novikov’s conjecture, Operator algebras and K-theory (San Francisco, 1981) (R. G. Douglas and C. Schochet, eds.), Contemp. Math., vol. 10, Amer. Math. Soc., Providence, RI, 1982, pp. 77–98.

[HsS] W.-C. Hsiang and J. Shaneson, Fake tori, the annulus conjecture, and the conjectures of Kirby, Proc. Nat. Acad. Sci. U.S.A. 62 (1969), 687–691.

[Hu] B. Hu, Whitehead groups of finite polyhedra with nonpositive curvature, J. Diff. Geom. 38 (1993), 501–517.

[HugTW] E. B. Hughes, L. R. Taylor and E. B. Williams, Rigidity of fibrations over nonpositively curved manifolds, Topology 34 (1995), 565–574.

[Hu1] S. Hurder, Eta invariants and the odd index theorem for coverings, Geometric and topological invariants of elliptic operators (Bowdoin Coll., 1988) (J. Kaminker, ed.), Contemp. Math., vol. 105, Amer. Math. Soc., Providence, RI, 1990, pp. 47–82.

[Hu2] S. Hurder, Topology of covers and spectral theory of geometric operators, Index Theory and Operator Algebras (Boulder, CO, 1991) (J. Fox and P. Haskell, eds.), Contemp. Math., vol. 148, Amer. Math. Soc., Providence, RI, 1993, pp. 87–119.

[Hu3] S. Hurder, Exotic index theory and the Novikov Conjecture, Novikov Conjectures, Index Theorems and Rigidity, vol. 2 (S. Ferry, A. Ranicki, and J. Rosenberg, eds.), London Math. Soc. Lecture Notes, vol. 227, Cambridge Univ. Press, Cambridge, 1995, pp. 255–276.

[Hu4] S. Hurder, Exotic index theory for foliations, preprint, Univ. of Illinois at Chicago.

[Ji1] R. Ji, Smooth dense subalgebras of reduced group C^{∗}-algebras, Schwartz cohomology of groups, and cyclic cohomology, J. Functional Analysis 107 (1992), 1–33.

[Ji2] R. Ji, Some applications of cyclic cohomology to the study of group C^{∗}-algebras, Index Theory and Operator Algebras (Boulder, CO, 1991) (J. Fox and P.

Haskell, eds.), Contemp. Math., vol. 148, Amer. Math. Soc., Providence, RI, 1993, pp. 121–129.

[Ji3] R. Ji, Nilpotency of Connes’ periodicity operator and the idempotent conjectures, K-Theory 9 (1995), 59–76.

[Jo1] P. Jolissaint, K-theory of reduced C^{∗}-algebras and rapidly decreasing functions on groups, K-Theory 2 (1989), 723–736.

[Jo2] P. Jolissaint, Rapidly decreasing functions in reduced C^{∗}-algebras of groups, Trans. Amer. Math. Soc. 317 (1990), 167–196.

[Ju1] P. Julg, C^{∗}-algèbres associées à des complexes simpliciaux, C. R. Acad. Sci. Paris Sér. I Math. 308 (1989), 97–100.

[Ju2] P. Julg, K-théorie des C^{∗}-algèbres associées à certains groupes hyperboliques, Dissertation, Univ. Louis Pasteur, Publ. Inst. Recherche Math. Avancée, Univ. Louis Pasteur, Strasbourg, 1991.

[JuK] P. Julg and G. Kasparov, L’anneau KK_{G}(ℂ, ℂ) pour G = SU(n, 1), C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), 259–264.

[JuV] P. Julg and A. Valette, Fredholm modules associated to Bruhat-Tits buildings, Proc. Miniconferences on Harmonic Analysis and Operator Algebras (Canberra, 1987) (M. Cowling, C. Meaney, and W. Moran, eds.), Proc. Centre for Mathematical Analysis, vol. 16, Centre for Mathematical Analysis, Australian National Univ., Canberra, 1987, pp. 143–155.

[KM1] J. Kaminker and J. Miller, A comment on the Novikov conjecture, Proc. Amer. Math. Soc. 83 (1981), 656–658.

[KM2] J. Kaminker and J. Miller, Homotopy invariance of the analytic index of signature operators over C^{∗}-algebras, J. Operator Theory 14 (1985), 113–127.

[Kas1] G. G. Kasparov, A generalized index for elliptic operators, Funkc. Anal i Priložen. 7 no. 3 (1973), 82–83; English translation, Funct. Anal. Appl. 7 (1973), 238–240.

[Kas2] G. G. Kasparov, Topological invariants of elliptic operators, I: K-homology, Izv. Akad. Nauk SSSR, Ser. Mat. 39 (1975), 796–838; English translation, Math. USSR–Izv. 9 (1975), 751–792.

[Kas3] G. G. Kasparov, The operator K-functor and extensions of C^{∗}-algebras, Izv. Akad. Nauk SSSR, Ser. Mat. 44 (1980), 571–636; English translation, Math. USSR–Izv. 16 (1981), 513–572.

[Kas4] G. G. Kasparov, K-theory, group C^{∗}-algebras, and higher signatures: Conspectus, I, II, preprint, Inst. for Chemical Physics of the Soviet Acad. of Sci., Chernogolovka; reprinted with annotations,, Novikov Conjectures, Index Theorems and Rigidity, vol. 1 (S. Ferry, A. Ranicki, and J. Rosenberg, eds.), London Math. Soc. Lecture Notes, vol. 226, Cambridge Univ. Press, Cambridge, 1995, pp. 101–146.

[Kas5] G. G. Kasparov, Operator K-theory and its applications: elliptic operators, group representations, higher signatures, C^{∗}-extensions, Proc. International Congress of Mathematicians (Warsaw, 1983), vol. 2, Polish Scientific Publishers, Warsaw, 1984, pp. 987–1000.

[Kas6] G. G. Kasparov, Operator K-theory and its applications, Current problems in mathematics. Newest results, Itogi Nauki i Tekhniki, vol. 27, Akad. Nauk

SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1985, pp. 3–31.

[Kas7] , Equivariant KK-theory and the Novikov conjecture, Invent. Math. 91 (1988), 147–201.

[Kas8] , Novikov’s conjecture on higher signatures: the operator K-theory approach, Representation Theory of Groups and Algebras (J. Adams, R. Herb, S. Kudla, J.-S. Li, R. Lipsman, and J. Rosenberg, eds.), Contemporary Math., vol. 145, Amer. Math. Soc., Providence, 1993, pp. 79–100.

[KS1] G. G. Kasparov and G. Skandalis, Groupes agissant sur des immeubles de Bruhat-Tits, K-théorie operatorielle et conjecture de Novikov, C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), 171–174.

[KS2] G. G. Kasparov and G. Skandalis, Groups acting on buildings, operator K-theo-ry, and Novikov’s conjecture, K-Theory 4, Special issue in honor of A. Grothendieck (1991), 303–337.

[KS3] G. G. Kasparov and G. Skandalis, Groupes “boliques” et conjecture de Novikov, C. R. Acad. Sci. Paris Sér. I Math. 319 (1994), 815–820.

[Kato] T. Kato, Asymptotic Lipschitz cohomology and higher signatures, Geom. Funct. Anal. 6 (1996), 346–369.

[Kee] J. Keesling, The one-dimensional Čech cohomology of the Higson corona and its compactification, preprint, Univ. of Florida (1994).

[KerM] M. Kervaire and J. Milnor, Groups of homotopy spheres, I, Ann. of Math. 77 (1963), 504–537.

[KirS] R. Kirby and L. Siebenmann, Foundational Essays on Topological Manifolds, Smoothings, and Triangulations, Ann. of Math. Studies, vol. 88, Princeton Univ. Press, Princeton, NJ, 1977.

[Kis] J. Kister, Microbundles are fiber bundles, Ann. of Math. 80 (1964), 190–199.

[LaMi] H. B. Lawson, Jr. and M.-L. Michelsohn, Spin Geometry, Princeton Math. Ser., vol. 38, Princeton Univ. Press, Princeton, NJ, 1990.

[LeRa] N. Levitt and A. A. Ranicki, Intrinsic transversality structures, Pacific J. Math. 129 (1987), 85–144.

[Lod] J.-L. Loday, K-théorie algébrique et représentations des groupes, Ann. Sci. École Norm. Sup. (4) 9 (1976), 309–377.

[LodQ] J.-L. Loday and D. Quillen, Cyclic homology and the Lie algebra homology of matrices, Comment. Math. Helv. 59 (1984), 565–591.

[Lott] J. Lott, Superconnections and higher index theory, Geom. Funct. Anal. 4 (1992), 421–454.

[Lott] J. Lott, Higher eta-invariants, K-Theory 6 (1992), 191–233.

[Lus] G. Lusztig, Novikov’s higher signature and families of elliptic operators, J. Diff. Geom. 7 (1972), 229–256.

[Mac] M. Macho-Stadler, La conjecture de Baum-Connes pour un feuilletage sans holonomie de codimension un sur une variété fermée, Publ. Mat. 33 (1989), 445–457.

[Ma] I. Madsen, Reidemeister torsion, surgery invariants and spherical space forms, Proc. London Math. Soc. 46 (1983), 193–240.

[Mat1] V. Mathai, On the homotopy invariance of reduced eta and other signature type invariants, preprint, Univ. of Adelaide.

[Mat2] V. Mathai, Spectral flow, eta invariants, and von Neumann algebras, J. Funct. Anal. 109 (1992), 442–456.

[Milg] R. J. Milgram, Surgery with finite fundamental group, II: the oozing conjecture, Pacific J. Math. 151 (1991), 117–150.

[MilgR] R. J. Milgram and A. A. Ranicki, The L-theory of Laurent polynomial extensions and genus 0 function fields, J. reine angew. Math. 406 (1990), 121–166.

[Mill] J. Miller, Signature operators and surgery groups over C^{∗}-algebras, Preprint, Indiana Univ./Purdue Univ. (1992).

[Miln1] J. Milnor, On manifolds homeomorphic to the 7-sphere, Ann. of Math. 64 (1956), 399–405.

[Miln2] J. Milnor, A procedure for killing the homotopy groups of differentiable manifolds, Differential Geometry (Tucson, 1960) (C. B. Allendoerfer, ed.), Proc. Symp. Pure Math., vol. 3, 1961, pp. 39–55.

[Mis1] A. S. Mishchenko, Homotopy invariants of nonsimply connected manifolds, I: rational invariants, Izv. Akad. Nauk SSSR Ser. Mat. 34 (1970), 501–514; English translation, Math. USSR–Izv. 4 (1970), 506–519.

[Mis2] A. S. Mishchenko, Homotopy invariants of nonsimply connected manifolds, III: Higher signatures, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 1316–1355; Erratum , ibid. 36 (1972), 910.

[Mis3] A. S. Mishchenko, Infinite dimensional representations of discrete groups, and higher signatures, Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 81–106; English translation, Math. USSR–Izv. 8 (1974), 85–111.

[Mis4] A. S. Mishchenko, On Fredholm representations of discrete groups, Funkc. Anal i Priložen. 9 no. 2 (1975), 36–41; English translation, Funct. Anal. Appl. 9 (1975), 121–125.

[Mis5] A. S. Mishchenko, Hermitian K-theory. The theory of characteristic classes and methods of functional analysis, Uspekhi Mat. Nauk 31 no. 2 (188) (1976), 69–134; English translation, Russian Math. Surv. 31 no. 2 (1972), 71–138.

[Mis6] A. S. Mishchenko, C^{∗}-algebras and K-theory, Algebraic Topology, Århus 1978 (J. L. Dupont and I. Madsen, eds.), Lecture Notes in Math., vol. 763, Springer-Verlag, Berlin, Heidelberg, and New York, 1979, pp. 262–274.

[MisF] A. S. Mishchenko and A. T. Fomenko, The index of elliptic operators over C^{∗}-algebras, Izv. Akad. Nauk SSSR Ser. Mat. 43 (1979), 831–859; English translation, Math. USSR–Izv. 15 (1980), 87–112.

[MisS1] A. S. Mishchenko and Y. P. Soloviev, A classifying space for hermitian K-theo-ry, Trudy Sem. Vect. and Tensor Anal. 18 (1976), 140–168.

[MisS2] A. S. Mishchenko and Yu. P. Soloviev, Infinite-dimensional representations of fundamental groups, and formulas of Hirzebruch type, Dokl. Akad. Nauk SSSR 234 (1977), 761–764; English translation, Soviet Math. Dokl. 18 (1977), 767–771.

[MisS3] A. S. Mishchenko and Yu. P. Soloviev, Representations of Banach algebras and formulas of Hirzebruch type, Mat. Sb. 111(153) (1980), 209–226; English

translation, Math. USSR–Sb. 39 (1980), 189–205.

[Mos] H. Moscovici, Cyclic cohomology and invariants of multiply connected manifolds, Proc. International Congress of Mathematicians (Kyoto, 1990), vol. 1, Math. Soc. Japan, Tokyo, 1991, pp. 675–688.

[Na1] T. Natsume, The Baum-Connes conjecture, the commutator theorem, and Rieffel projections, C. R.-Math. Rep. Acad. Sci. Canada 10 (1988), 13–18.

[Na2] T. Natsume, Topological K-theory for codimension one foliations without holonomy, Foliations (Tokyo, 1983), Adv. Stud. Pure Math., vol. 5, 1985, pp. 15–27.

[Ne] W. D. Neumann, Signature-related invariants of manifolds, I: monodromy and γ-invariants, Topology 18 (1979), 147–160.

[Ni1] A. J. Nicas, Induction theorems for groups of homotopy manifold structures, Mem. Amer. Math. Soc. 39 no. 267 (1982).

[Ni2] A. J. Nicas, On Wh_{3} of a Bieberbach group, Math. Proc. Cambridge Philos. Soc. 95 (1984), 55–60.

[Ni3] A. J. Nicas, On the higher Whitehead groups of a Bieberbach group, Trans. Amer. Math. Soc. 287 (1985), 853–859.

[Nis1] V. Nistor, Group cohomology and the cyclic cohomology of crossed products, Invent. Math. 99 (1990), 411–424.

[Nis2] V. Nistor, Cyclic cohomology of crossed products by algebraic groups, Invent. Math. 112 (1993), 615–638.

[Nov1] S. P. Novikov, Diffeomorphisms of simply connected manifolds, Dokl. Akad. Nauk SSSR 143 (1962), 1046–1049; English translation, Soviet Math. Dokl. 3 (1962), 540–543.

[Nov2] S. P. Novikov, Homotopically equivalent smooth manifolds. I, Izv. Akad. Nauk SSSR, Ser. Mat. 28 (1964), 365–474; English translation, Amer. Math. Soc. Transl. (2) 48 (1965), 271–396.

[Nov3] S. P. Novikov, Rational Pontrjagin classes. Homeomorphism and homotopy type of closed manifolds. I, Izv. Akad. Nauk SSSR, Ser. Mat. 29 (1965), 1373–1388.

[Nov4] S. P. Novikov, The homotopy and topological invariance of certain rational Pontrjagin classes, Dokl. Akad. Nauk SSSR 162 (1965), 1248–1251; English translation, Soviet Math. Dokl. 6 (1965), 854–857.

[Nov5] S. P. Novikov, Topological invariance of rational classes of Pontrjagin, Dokl. Akad. Nauk SSSR 163 (1965), 298–300; English translation, Soviet Math. Dokl. 6 (1965), 921–923.

[Nov6] S. P. Novikov, On manifolds with free abelian fundamental group and their application, Izv. Akad. Nauk SSSR, Ser. Mat. 30 (1966), 207–246; English translation, Amer. Math. Soc. Transl. (2) 71 (1968), 1–42.

[Nov7] S. P. Novikov, Pontrjagin classes, the fundamental group and some problems of stable algebra, Proc. International Congress of Mathematicians (Moscow, 1966), Amer. Math. Soc. Transl. (2), vol. 70, Amer. Math. Soc., Providence, RI, 1968, pp. 172–179.

[Nov8] S. P. Novikov, Analogues hermitiens de la K-théorie, Actes du Congrès International des Mathématiciens (Nice, 1970), vol. 2, Gauthier-Villars, Paris,

pp. 39–45.

[Nov9] S. P. Novikov, Pontrjagin classes, the fundamental group and some problems of stable algebra, Essays on Topology and Related Topics (Mémoires dédiés à Georges de Rham) (A. Haefliger and R. Narasimhan, eds.), Springer-Verlag, New York, Heidelberg, and Berlin, 1970, pp. 147–155.

[Nov10] S. P. Novikov, Algebraic construction and properties of Hermitian analogues of K-theory over rings with involution from the viewpoint of the Hamiltonian formalism. Applications to differential topology and the theory of characteristic classes, Izv. Akad. Nauk SSSR, Ser. Mat. 34 (1970), 253–288, 475–500; English translation, Math. USSR–Izv. 4 (1970), 257–292, 479–505.

[Ogle1] C. Ogle, Assembly maps, K-theory, and hyperbolic groups, K-Theory 6 (1992), 235–265.

[Ogle2] C. Ogle, Simplicial rapid decay algebras associated to a discrete group, Preprint, Ohio State Univ., 1995.

[Ogle3] C. Ogle, Filtrations of simplicial functors, topological K-theory and the strong Novikov conjecture, Preprint, Ohio State Univ., 1995.

[Ogle4] C. Ogle, Filtrations of simplicial functors, topological K-theory and the Baum-Connes conjecture, Preprint, Ohio State Univ., 1996.

[Pe1] E. K. Pedersen, On the bounded and thin h-cobordism theorem parametrized by ℝ^{k}, Transformation Groups, Poznań 1985 (S. Jackowski and K. Pawałowski, eds.), Lecture Notes in Math., vol. 1217, Springer-Verlag, Berlin, Heidelberg, and New York, 1986, pp. 306–320.

[Pe2] E. K. Pedersen, Bounded and continuous control, Novikov Conjectures, Index Theorems and Rigidity, vol. 2 (S. Ferry, A. Ranicki, and J. Rosenberg, eds.), London Math. Soc. Lecture Notes, vol. 227, Cambridge Univ. Press, Cambridge, 1995, pp. 277–284.

[PeRW] E. K. Pedersen, J. Roe and S. Weinberger, On the homotopy invariance of the boundedly controlled analytic signature of a manifold over an open cone, Novikov Conjectures, Index Theorems and Rigidity, vol. 2 (S. Ferry, A. Ranicki, and J. Rosenberg, eds.), London Math. Soc. Lecture Notes, vol. 227, Cambridge Univ. Press, Cambridge, 1995, pp. 285–300.

[PeW] E. K. Pedersen and C. Weibel, K-theory homology of spaces, Algebraic Topology, Proc., 1986 (G. Carlsson R. L. Cohen, H. R. Miller, and D. C. Ravenel, eds.), Lecture Notes in Math., vol. 1370, Springer-Verlag, Berlin, Heidelberg, and New York, 1989, pp. 346–361.

[Pet] M. E. Petty, Waldhausen’s theory of k-fold end structures, Topology Appl. 14 (1982), 71–85.

[Pim1] M. Pimsner, KK-groups of crossed products by groups acting on trees, Invent. Math. 86 (1986), 603–634.

[Pim2] M. Pimsner, K-theory for groups acting on trees, Proc. International Congress of Mathematicians (Kyoto, 1990), vol. 1, Math. Soc. Japan, Tokyo, 1991, pp. 979–986.

[PimV1] M. Pimsner and D. Voiculescu, Exact sequences for K-groups and Ext-groups for certain cross products of C^{∗}-algebras, J. Operator Theory 4 (1980), 93–118.

[PimV2] M. Pimsner and D. Voiculescu, K-groups of reduced crossed products by free

groups, J. Operator Theory 8 (1982), 131–156.

[Pl1] R. Plymen, K-theory for the reduced C^{∗}-algebra of SL_{2}(ℚ_{p}), Operator Algebras and their Connections with Topology and Ergodic Theory (H. Araki, C. C. Moore, Ş. Strătilă and D. Voiculescu, eds.), Lect. Notes in Math., vol. 1132, Springer-Verlag, Berlin, Heidelberg, New York, 1985, pp. 409–420.

[Pl2] R. Plymen, Reduced C^{∗}-algebra of the p-adic group GL(n), J. Funct. Anal. 72 (1987), 1–12.

[Pl3] R. Plymen, Reduced C^{∗}-algebra for reductive p-adic groups, J. Funct. Anal. 88 (1990), 251–266.

[Q1] F. Quinn, A geometric formulation of surgery, Topology of manifolds (Athens, Ga. 1969) (J. C. Cantrell and C. H. Edwards, ed.), Markham Math. Ser., Markham Press, Chicago, 1970, pp. 500–511.

[Q2] F. Quinn, B_{(T OP_{n})^{∼}} and the surgery obstruction, Bull. Amer. Math. Soc. 77 (1971), 596–600.

[Q3] F. Quinn, Ends of maps, II, Invent. Math. 68 (1982), 353–424.

[Q4] F. Quinn, Algebraic K-theory of poly-(finite or cyclic) groups, Bull. Amer. Math. Soc. 12 (1985), 221–226.

[Q5] F. Quinn, Applications of topology with control, Proc. International Congress of Mathematicians (Berkeley, Calif., 1986), vol. 1, Amer. Math. Soc., Providence, RI, 1987, pp. 598–606.

[Q6] F. Quinn, Homotopically stratified spaces, J. Amer. Math. Soc. 1 (1988), 441– 499.

[Q7] F. Quinn, Assembly maps in bordism-type theories, Novikov Conjectures, Index Theorems and Rigidity, vol. 1 (S. Ferry, A. Ranicki, and J. Rosenberg, eds.), London Math. Soc. Lecture Notes, vol. 226, Cambridge Univ. Press, Cambridge, 1995, pp. 201–271.

[Ran1] A. Ranicki, Algebraic L-theory I. Foundations, Proc. London Math. Soc. 27 (1973), 101–125.

[Ran2] A. Ranicki, Algebraic L-theory II. Laurent extensions, Proc. London Math. Soc. 27 (1973), 126–158.

[Ran3] A. Ranicki, Algebraic L-theory III. Twisted Laurent extensions, Hermitian K-Theory and Geometric Applications (H. Bass, ed.), Lecture Notes in Math., vol. 343, Springer-Verlag, Berlin, Heidelberg, and New York, 1973, pp. 412–463.

[Ran4] A. Ranicki, The algebraic theory of surgery I. Foundations, Proc. London Math. Soc. 40 (1980), 87–192.

[Ran5] A. Ranicki, The algebraic theory of surgery II. Applications to topology, Proc. London Math. Soc. 40 (1980), 193–283.

[Ran6] A. Ranicki, The total surgery obstruction, Algebraic topology, Aarhus 1978, Lecture Notes in Math., vol. 763, Springer-Verlag, Berlin, Heidelberg, New York, 1979, pp. 275–316.

[Ran7] A. Ranicki, Exact Sequences in the Algebraic Theory of Surgery, Princeton Math. Notes, vol. 26, Princeton Univ. Press, Princeton, 1981.

[Ran8] A. Ranicki, Lower K- and L-Theory, London Math. Soc. Lecture Notes, vol. 178, Cambridge Univ. Press, Cambridge, 1992.

[Ran9] A. Ranicki, Algebraic L-Theory and Topological Manifolds, Cambridge Tracts in Math., vol. 102, Cambridge Univ. Press, Cambridge, 1992.

[Ran10] A. Ranicki, On the Novikov Conjecture, Novikov Conjectures, Index Theorems and Rigidity, vol. 1 (S. Ferry, A. Ranicki, and J. Rosenberg, eds.), London Math. Soc. Lecture Notes, vol. 226, Cambridge Univ. Press, Cambridge, 1995, pp. 272–337.

[Ran11] A. Ranicki (editor), The Hauptvermutung Book, papers by A. J. Casson, D. P. Sullivan, M. A. Armstrong, G. E. Cooke, C. P. Rourke and A. A. Ranicki, K-Theory book series, vol. 1 (to appear).

[Roe1] J. Roe, An index theorem on open manifolds, I, J. Diff. Geom. 27 (1988), 87–113; II, ibid., 115–136.

[Roe2] J. Roe, Hyperbolic metric spaces and the exotic cohomology Novikov conjecture, K-Theory 4 (1990), 501–512; Erratum, ibid. 5 (1991), 189.

[Roe3] J. Roe, Coarse cohomology and index theory on complete Riemannian manifolds, Mem. Amer. Math. Soc. no. 497 (1993).

[Rokh] V. A. Rokhlin, Pontrjagin-Hirzebruch class of codimension 2, Izv. Akad. Nauk SSSR Ser. Mat. 30 (1966), 705–718.

[RokS] V. A. Rokhlin and A. S. Shvarts, The combinatorial invariance of Pontrjagin classes, Dokl. Akad. Nauk SSSR 114 (1957), 490–493.

[Ros1] J. Rosenberg, Group C^{∗}-algebras and topological invariants, Operator algebras and group representations, Vol. II (Neptun, 1980), Monographs Stud. Math., vol. 18, Pitman, Boston and London, 1984, pp. 95–115.

[Ros2] J. Rosenberg, C^{∗}-algebras, positive scalar curvature, and the Novikov conjecture, Publ. Math. Inst. Hautes Études Sci. 58 (1983), 197–212.

[Ros3] J. Rosenberg, C^{∗}-algebras, positive scalar curvature, and the Novikov conjecture, II, Geometric methods in operator algebras (Kyoto, 1983) (H. Araki and E. G. Effros, eds.), Pitman Res. Notes Math., vol. 123, Longman Sci. Tech., Harlow, 1986, pp. 341–374.

[Ros4] J. Rosenberg, C^{∗}-algebras, positive scalar curvature, and the Novikov conjecture, III, Topology 25 (1986), 319–3362.

[Ros5] J. Rosenberg, The KO-assembly map and positive scalar curvature, Algebraic Topology, Poznań 1989 (S. Jackowski, B. Oliver, and K. Pawałowski, eds.), Lecture Notes in Math., vol. 1474, Springer-Verlag, Berlin, Heidelberg, and New York, 1991, pp. 170–182.

[Ros6] J. Rosenberg, Analytic Novikov for topologists, Novikov Conjectures, Index Theorems and Rigidity, vol. 1 (S. Ferry, A. Ranicki, and J. Rosenberg, eds.), London Math. Soc. Lecture Notes, vol. 226, Cambridge Univ. Press, Cambridge, 1995, pp. 338–372.

[RS1] J. Rosenberg and S. Stolz, Manifolds of positive scalar curvature, Algebraic Topology and its Applications (G. Carlsson, R. Cohen, W.-C. Hsiang, and J. D. S. Jones, eds.), M. S. R. I. Publications, vol. 27, Springer-Verlag, New York, 1994, pp. 241–267.

[RS2] J. Rosenberg and S. Stolz, A “stable” version of the Gromov-Lawson conjecture, The Čech Centennial: Proc. Conf. on Homotopy Theory (M. Cenkl and H. Miller, eds.), Contemp. Math., vol. 181, Amer. Math. Soc., Providence, RI, 1995, pp. 405–418.

[RS3] J. Rosenberg and S. Stolz, Metrics of Positive Scalar Curvature, DMV-Seminar, Birkhäuser, Basel, Boston, in preparation.

[RW1] J. Rosenberg and S. Weinberger, Higher G-indices and applications, Ann. Sci. École Norm. Sup. 21 (1988), 479–495.

[RW2] J. Rosenberg and S. Weinberger, An equivariant Novikov conjecture, with an appendix by J. P. May, K-Theory 4, Special issue in honor of A. Grothendieck (1990), 29–53.

[RW3] J. Rosenberg and S. Weinberger, Higher G-signatures for Lipschitz manifolds, K-Theory 7 (1993), 101–132.

[Sh1] J. Shaneson, Wall’s surgery obstruction groups for ℤ × G, for suitable groups G, Bull. Amer. Math. Soc. 74 (1968), 467–471.

[Sh2] J. Shaneson, Wall’s surgery obstruction groups for ℤ × G, Ann. of Math. 90 (1969), 296–334.

[Shar] B. L. Sharma, Topologically invariant characteristic classes, Topology Appl. 21 (1985), 135–146.

[SharSi] B. L. Sharma and N. Singh, Topological invariance of integral Pontrjagin classes mod p, Topology Appl. 63 (1995), 59–67.

[Si] N. Singh, On topological and homotopy invariance of integral Pontrjagin classes modulo a prime p, Topology Appl. 38 (1991), 225–235.

[Sk1] G. Skandalis, Kasparov’s bivariant K-theory and applications, Expositiones Math. 9 (1991), 193–250.

[Sk2] G. Skandalis, Approche de la conjecture de Novikov par la cohomologie cyclique (d’après A. Connes, M. Gromov et H. Moscovici), Séminaire Bourbaki, 1990–91, exposé no. 739, Astérisque 201–203 (1992), 299–320.

[So] Yu. P. Soloviev, A theorem of Atiyah-Hirzebruch type for infinite groups, Vestnik Moskov. Univ., Ser. I–Mat. Meh. 30 no. 4 (1975), 26–35; English translation, Moscow Univ. Math. Bull. 30 no. 3/4 (1975), 77–85.

[Spv] M. Spivak, Spaces satisfying Poincaré duality, Topology 6 (1967), 77–102.

[St] S. Stolz, Positive scalar curvature metrics — existence and classification questions, Proc. International Congress of Mathematicians, Zürich 1994, vol. 1 (S. D. Chatterji, ed.), Birkhäuser, Basel, 1995, pp. 625–636.

[Sul] D. Sullivan, Triangulating homotopy equivalences, Ph.D. dissertation, Princeton Univ., Princeton, 1965.

[Tak1] H. Takai, A counterexample of strong Baum-Connes conjectures for foliated manifolds, Mappings of operator algebras (Philadelphia, PA, 1988), Progress in Math., vol. 84, Birkhäuser, Boston, 1990, pp. 183–197.

[Tak2] H. Takai, Baum-Connes conjectures and their applications, Dynamical systems and applications (Kyoto, 1987), World Sci. Adv. Ser. Dyn. Syst., vol. 5, World Sci., Singapore, 1987, pp. 89–116.

[Tak3] H. Takai, On the Baum-Connes conjecture, The study of dynamical systems (Kyoto, 1989), World Sci. Adv. Ser. Dyn. Syst., vol. 7, World Sci., Teaneck, NJ, 1989, pp. 149–154.

[TaW] L. Taylor and B. Williams, Surgery spaces: formulae and structure, Algebraic topology, Waterloo, 1978, Lecture Notes in Math., vol. 741, Springer-Verlag, Berlin, Heidelberg, New York, 1979, pp. 170–195.

[Th1] R. Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954), 17–86.

[Th2] R. Thom, Les classes caractéristiques de Pontrjagin des variétés triangulées, Proc. Symp. Internacional de Topologica Algebraica, Univ. Nacional Autonoma de México, Mexico City, 1958, pp. 54–67.

[Ths1] C. B. Thomas, Splitting theorems for certain PD^{3}-groups, Math. Z. 186 (1984), 201–209.

[Ths2] C. B. Thomas, 3-manifolds and PD(3)-groups, Novikov Conjectures, Index Theorems and Rigidity, vol. 2 (S. Ferry, A. Ranicki, and J. Rosenberg, eds.), London Math. Soc. Lecture Notes, vol. 227, Cambridge Univ. Press, Cambridge, 1995, pp. 301–308.

[Ti] U. Tillmann, K-theory of fine topological algebras, Chern character, and assembly, K-Theory 6 (1992), 57–86.

[To] A. M. Torpe, K-theory for the leaf space of foliations by Reeb components, J. Funct. Anal. 61 (1985), 15–71.

[Tr1] E. V. Troitsky, The index of the generalized Hirzebruch operator and the homotopically invariant higher signatures, Selected topics in Algebra, Geometry and Discr. Math., Moscow State Univ., Moscow, 1992, pp. 151–152.

[Tr2] E. V. Troitsky, The Hirzebruch operator on P L manifolds and the higher signatures, Uspekhi Mat. Nauk 48 no. 1 (1993), 189–190; English translation, Russian Math. Surv. 48 no. 1 (1993), 197–198.

[Tsy] B. L. Tsygan, Homology of matrix Lie algebras over rings and Hochschild homology, Uspekhi Mat. Nauk 38 no. 2 (1983), 217–218; English translation, Russian Math. Surv. 38 no. 2 (1983), 198–199.

[Va] A. Valette, Le rôle des fibrés de rang fini en théorie de Kasparov équivariante, Mem. Acad. Roy. Belg., Classes des Sciences (1986).

[Vi] M. F. Vigneras, Homologie cyclique, principe de Selberg et pseudo-coefficient, Invent. Math. 116 (1994), 651–676.

[Vog] W. Vogell, Continuously controlled A-theory, K-theory 9 (1995), 567–576.

[Wald1] F. Waldhausen, Algebraic K-theory of amalgamated free products, Ann. of Math. 108 (1978), 135–256.

[Wald2] F. Waldhausen, Algebraic K-theory of topological spaces, I, Algebraic and Geometric Topology (Stanford, 1976), Proc. Symp. Pure Math., vol. 32, Amer. Math. Soc., Providence, RI, 1978, pp. 35–60; II, Algebraic topology, Aarhus 1978, Lecture Notes in Math., vol. 763, Springer-Verlag, Berlin, Heidelberg, New York, 1979, pp. 356–394.

[Wald3] F. Waldhausen, Algebraic K-theory of spaces, a manifold approach, Current Trends in Algebraic Topology, Part 1 (London, Ont., 1981), Canad. Math. Soc. Conf. Proc., vol. 2, Amer. Math. Soc., Providence, RI, 1982, pp. 141–184.

[Wall1] C. T. C. Wall, Surgery of non-simply-connected manifolds, Ann. of Math. 84 (1966), 217–276.

[Wall2] C. T. C. Wall, Surgery on Compact Manifolds, London Math. Soc. Monographs, vol. 1, Academic Press, London and New York, 1970.

[Was] A. Wassermann, A proof of the Connes-Kasparov conjecture for connected reductive linear Lie groups, C. R. Acad. Sci. Paris Sér. I Math. 304 (1987), 559–562.

[W1] S. Weinberger, The Novikov conjecture and low-dimensional topology, Comment. Math. Helv. 58 (1983), 355–364.

[W2] S. Weinberger, Constructions of group actions: a survey of some recent developments, Group actions on manifolds (Boulder, Colo., 1983) (R. Schultz, ed.), Contemp. Math., vol. 36, Amer. Math. Soc., Providence, RI, 1985, pp. 269–298.

[W3] S. Weinberger, Group actions and higher signatures, Proc. Nat. Acad. Sci. U.S.A. 82 (1985), 1297–1298.

[W4] S. Weinberger, Homologically trivial group actions, II: nonsimply connected manifolds, Amer. J. Math. 108 (1986), 1259–1275.

[W5] S. Weinberger, Group actions and higher signatures, II, Comm. Pure Appl. Math. 40 (1987), 179–187.

[W6] S. Weinberger, Class numbers, the Novikov Conjecture, and transformation groups, Topology 27 (1988), 353–365.

[W7] S. Weinberger, Homotopy invariance of eta invariants, Proc. Nat. Acad. Sci. U.S.A. 85 (1988), 5362–5363.

[W8] S. Weinberger, Aspects of the Novikov conjecture, Geometric and topological invariants of elliptic operators (Bowdoin Coll., 1988) (J. Kaminker, ed.), Contemp. Math., vol. 105, Amer. Math. Soc., Providence, RI, 1990, pp. 281–297.

[W9] S. Weinberger, The Topological Classification of Stratified Spaces, Chicago Lectures in Math., Univ. of Chicago Press, Chicago, 1994.

[W10] S. Weinberger, Nonlocally linear manifolds and orbifolds, Proc. International Congress of Mathematicians (Zürich, 1994) (S. D. Chatterji, ed.), Birkhäuser, 1996.

[Weis] M. Weiss, The Novikov Conjecture for classes of finite length, Preprint, Univ. of Notre Dame, 1996.

[WW1] M. Weiss and B. Williams, Automorphisms of manifolds and algebraic K-theory: I, K-Theory 1 (1988), 575–626.

[WW2] M. Weiss and B. Williams, Automorphisms of manifolds and algebraic K-theory: II, J. Pure and Appl. Algebra 62 (1989), 47–107.

[WW3] M. Weiss and B. Williams, Automorphisms of manifolds and algebraic K-theory: Finale, Preprint, Univ. of Notre Dame, 1994, 62pp.

[WW4] M. Weiss and B. Williams, Assembly, Novikov Conjectures, Index Theorems and Rigidity, vol. 2 (S. Ferry, A. Ranicki, and J. Rosenberg, eds.), London Math. Soc. Lecture Notes, vol. 227, Cambridge Univ. Press, Cambridge, 1995, pp. 332–352.

[WW5] M. Weiss and B. Williams, Pro-excisive functors, Novikov Conjectures, Index Theorems and Rigidity, vol. 2 (S. Ferry, A. Ranicki, and J. Rosenberg, eds.), London Math. Soc. Lecture Notes, vol. 227, Cambridge Univ. Press, Cambridge, 1995, pp. 353–364.

[Wu] F. Wu, The higher index theorem for manifolds with boundary, J. Funct. Anal. 103 (1992), 160–189.

[Ya1] M. Yamasaki, L-groups of crystallographic groups, Invent. Math. 88 (1987), 571–602.

[Ya2] M. Yamasaki, L-groups of virtually polycyclic groups, Topology and Appl. 33 (1989), 223–233.

[Ya3] M. Yamasaki, Maps between orbifolds, Proc. Amer. Math. Soc. 109 (1990), 223–232; Erratum, ibid. 115 (1992), 875.

[Yo] M. Yoshida, Surgery obstruction of twisted products, Math. J. Okayama Univ. 24 (1982), 73–97.

[Yu1] G. Yu, K-theoretic indices of Dirac-type operators on complete manifolds and the Roe algebra, preprint, Univ. of Colorado, 1991.

[Yu2] G. Yu, Cyclic cohomology and higher indices for noncompact complete manifolds, J. Funct. Anal. 133 (1995), 442–473.

[Yu3] G. Yu, Baum-Connes conjecture and coarse geometry, K-Theory 9 (1995), 223–232.

[Yu4] G. Yu, Coarse Baum-Connes conjecture, K-Theory 9 (1995), 199-222.

[Yu5] G. Yu, Zero-in-the-spectrum conjecture, positive scalar curvature and asymptotic dimension, preprint, Univ. of Colorado, 1995.

[Yu6] G. Yu, The Novikov conjecture and groups with finite asymptotic dimension, preprint, Univ. of Colorado, 1995.

Department of Mathematical Sciences, SUNY at Binghamton, Binghamton, NY 13901, U.S.A.

email : steve@math.binghamton.edu

Department of Mathematics and Statistics, James Clerk Maxwell Bldg., University of Edinburgh, Edinburgh EH9 3JZ, Scotland, U.K.

email : a.ranicki@edinburgh.ac.uk

Department of Mathematics, University of Maryland, College Park, MD 20742, U.S.A.

email : jmr@math.umd.edu