Volume 7, issue 1 (2003)

Download this article
For printing
Recent Issues

Volume 22
Issue 7, 3761–4380
Issue 6, 3145–3760
Issue 5, 2511–3144
Issue 4, 1893–2510
Issue 3, 1267–1891
Issue 2, 645–1266
Issue 1, 1–644

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Other MSP Journals
On invariants of Hirzebruch and Cheeger–Gromov

Stanley Chang and Shmuel Weinberger

Geometry & Topology 7 (2003) 311–319

arXiv: math.GT/0306247

Abstract

We prove that, if M is a compact oriented manifold of dimension 4k + 3, where k > 0, such that π1(M) is not torsion-free, then there are infinitely many manifolds that are homotopic equivalent to M but not homeomorphic to it. To show the infinite size of the structure set of M, we construct a secondary invariant τ(2): S(M) that coincides with the ρ–invariant of Cheeger–Gromov. In particular, our result shows that the ρ–invariant is not a homotopy invariant for the manifolds in question.

Keywords
signature, $L^2$–signature, structure set, $\rho$–invariant
Mathematical Subject Classification 2000
Primary: 57R67
Secondary: 46L80, 58G10
References
Forward citations
Publication
Received: 28 March 2003
Accepted: 30 April 2003
Published: 17 May 2003
Proposed: Stephen Ferry
Seconded: Ronald Stern, Benson Farb
Authors
Stanley Chang
Department of Mathematics
Wellesley College
Wellesley
Massachusetts 02481
USA
Shmuel Weinberger
Department of Mathematics
University of Chicago
Chicago
Illinois 60637
USA