Geometry & Topology, Vol. 7 (2003) Paper no. 9, pages 311--319.

On Invariants of Hirzebruch and Cheeger-Gromov

Stanley Chang, Shmuel Weinberger

Abstract. We prove that, if M is a compact oriented manifold of dimension 4k+3, where k>0, such that pi_1(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 tau_(2): S(M)-->R that coincides with the rho-invariant of Cheeger-Gromov. In particular, our result shows that the rho-invariant is not a homotopy invariant for the manifolds in question.

Keywords. Signature, L^2-signature, structure set, rho-invariant

AMS subject classification. Primary: 57R67. Secondary: 46L80, 58G10.

DOI: 10.2140/gt.2003.7.311

E-print: arXiv:math.GT/0306247

Submitted to GT on 28 March 2003. Paper accepted 30 April 2003. Paper published 17 May 2003.

Notes on file formats

Stanley Chang, Shmuel Weinberger

Department of Mathematics, Wellesley College
Wellesley, MA 02481, USA
Department of Mathematics, University of Chicago
Chicago, IL 60637, USA


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