Novikov Conjecture Home Page
The intended function of this home page is to keep you uptodate
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," coedited
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 0521497965 and ISBN 0521497957. 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 the texts of important previously unpublished classic papers by Milnor,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 Ktheory
and the assembly map in algebraic Ktheory" 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 Ltheory and Topological Manifolds"
by Andrew A. Ranicki, Cambridge Tracts in Mathematics, vol. 102,
Cambridge Univ. Press, 1993, 358 pp.,
Hardback, ISBN 0521420245, $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 Ltheory.
Contents: Part I: Algebra/ Algebraic Poincaré Complexes/ Algebraic Normal
Complexes/ Algebraic Normal Categories/ Categories Over Complexes/ Duality/
Simplyconnected Assembly/ Derived Products and Hom/ Local Poincaré
Duality/
Universal Assembly/ The Algebraic pipi Theorem/ Deltasets/
Generalised Homology
Theory/ Algebraic Lspectra/ The Algebraic Surgery Exact Sequence/ Connective
Ltheory/ Part II: Topology/ The Ltheory Orientation of Topology/ The Total
Surgery Obstruction/ The Structure Set/ Geometric Poincaré
Complexes/ The
Simplyconnected Case/ Transfer/ Finite Fundamental Group/ Splitting/ Higher
Signatures/ Periodicity/ Surgery with Coefficients/ Appendix A: The Nonorientable
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 0226885666.
Paper, $18.95tx, ISBN 0226885674. 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",
coedited by Simon Gindikin, James Lepowsky, and Robert Wilson,
Progress in Mathematics, vols. 131132,
Birkhäuser,
Boston, 1996.
Volume 1: Appr. 320 pp., 18 illus., hardcover, $54.50, ISBN
0817637559.
Volume 2: Appr. 380 pp., 23 illus., hardcover, $54.50, ISBN
0817638555.
Two Volume Set: $84.50, ISBN 0817638601.
Volume 2 is largely devoted to the massive paper
Positive Curvature, Macroscopic Dimension, Spectral Gaps, and Higher
Signatures by M. Gromov (pages 1213), which deals in large part
with issues connected with the Novikov Conjecture.
Some relevant preprint servers: