Novikov Conjecture Home Page
The intended function of this home page is to keep you up-to-date
on the latest developments concerning the Novikov Conjecture and
related problems in topology, geometry, algebra,
and analysis. Further contributions
of all sorts are welcome. Please send them to Jonathan Rosenberg at
jmr@math.umd.edu
Bibliography on the Novikov Conjecture and related topics:
This bibliography is based on the one in "A history and survey of
the Novikov Conjecture" by Steve Ferry, Andrew Ranicki, and Jonathan
Rosenberg. The original version appeared in volume 1 of
"Novikov Conjectures, Index Theorems and Rigidity" (listed below under books)
but we will try to update it regularly. To view the dvi file
(approx. 80kb), click
here.
For a tar'ed dvi file (better suited for downloading), click
here.
Some recent books:
-
"Novikov Conjectures, Index Theorems and Rigidity," co-edited
by Steve Ferry,
Andrew Ranicki, and
Jonathan Rosenberg,
London Math. Soc. Lecture Notes,
vols. 226 and 227 (approx. 380 pages each),
Cambridge Univ. Press,
1995. Paperback, $39.95 per volume.
ISBN 0-521-49796-5 and ISBN 0-521-49795-7. These volumes are
the outgrowth of a conference held at the Mathematisches Forschungsinstitut
Oberwolfach (Germany) in September, 1993. Volume I contains
- A detailed historical survey and bibliography of the Novikov Conjecture
and of related subsequent developments, including an annotated reprint
(both in the Russian original and in English translation) of
Novikov's original 1970 statement of his conjecture;
- an annotated problem list;
- the texts of important previously unpublished classic papers by Milnor,
Browder, and Kasparov; and
- research/survey papers on the Novikov Conjecture by Ferry/Weinberger,
Gromov, Mishchenko, Quinn, Ranicki, and Rosenberg.
Volume II contains
- fundamental long research papers by G. Carlsson on "Bounded K-theory
and the assembly map in algebraic K-theory" and by S. Ferry and
E. Pedersen on "Epsilon surgery theory";
- shorter research and survey papers on various topics related to the
Novikov Conjecture, by Bekka/Cherix/Valette, Eichhorn, Ferry, Higson/Roe,
Hurder, Pedersen, Pedersen/Roe/Weinberger, Thomas, Troitsky, and
Weiss/Williams.
For complete tables of contents of these volumes,
click here for a dvi file and
here for postscript.
For errata to these volumes,
click here for a dvi file and
here for postscript.
-
"Algebraic L-theory and Topological Manifolds"
by Andrew A. Ranicki, Cambridge Tracts in Mathematics, vol. 102,
Cambridge Univ. Press, 1993, 358 pp.,
Hardback, ISBN 0-521-42024-5, $69.95. This book explains the
applications of quadratic forms to the classification of topological manifolds, in a
unified algebraic framework. While not explicitly about the Novikov
Conjecture, it does deal extensively with the assembly map in L-theory.
Contents: Part I: Algebra/ Algebraic Poincaré Complexes/ Algebraic Normal
Complexes/ Algebraic Normal Categories/ Categories Over Complexes/ Duality/
Simply-connected Assembly/ Derived Products and Hom/ Local Poincaré
Duality/
Universal Assembly/ The Algebraic pi-pi Theorem/ Delta-sets/
Generalised Homology
Theory/ Algebraic L-spectra/ The Algebraic Surgery Exact Sequence/ Connective
L-theory/ Part II: Topology/ The L-theory Orientation of Topology/ The Total
Surgery Obstruction/ The Structure Set/ Geometric Poincaré
Complexes/ The
Simply-connected Case/ Transfer/ Finite Fundamental Group/ Splitting/ Higher
Signatures/ Periodicity/ Surgery with Coefficients/ Appendix A: The Non-orientable
Case/ Appendix B: Assembly Via Products/ Appendix C: Assembly Via Control
For an extensive review of this book by S. Weinberger, click here.
-
"The Topological Classification of Stratified Spaces"
by Shmuel Weinberger,
The University of Chicago Press,
1994. xiv, 284 p., 15 line drawings.
Cloth, $47.50tx, ISBN 0-226-88566-6.
Paper, $18.95tx, ISBN 0-226-88567-4. This book discusses surgery theory
and how it can be extended to stratified spaces. There is considerable discussion
of the Novikov Conjecture and its analogues and variants.
- "Functional Analysis on the Eve of the 21st Century:
In Honor of I. M. Gelfand's 80th Birthday",
co-edited by Simon Gindikin, James Lepowsky, and Robert Wilson,
Progress in Mathematics, vols. 131-132,
Birkhäuser,
Boston, 1996.
Volume 1: Appr. 320 pp., 18 illus., hardcover, $54.50, ISBN
0-8176-3755-9.
Volume 2: Appr. 380 pp., 23 illus., hardcover, $54.50, ISBN
0-8176-3855-5.
Two Volume Set: $84.50, ISBN 0-8176-3860-1.
Volume 2 is largely devoted to the massive paper
Positive Curvature, Macroscopic Dimension, Spectral Gaps, and Higher
Signatures by M. Gromov (pages 1-213), which deals in large part
with issues connected with the Novikov Conjecture.
Some relevant preprint servers: