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2003 On invariants of Hirzebruch and Cheeger–Gromov
Stanley Chang, Shmuel Weinberger
Geom. Topol. 7(1): 311-319 (2003). DOI: 10.2140/gt.2003.7.311

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.

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Stanley Chang. Shmuel Weinberger. "On invariants of Hirzebruch and Cheeger–Gromov." Geom. Topol. 7 (1) 311 - 319, 2003. https://doi.org/10.2140/gt.2003.7.311

Information

Received: 28 March 2003; Accepted: 30 April 2003; Published: 2003
First available in Project Euclid: 21 December 2017

zbMATH: 1037.57028
MathSciNet: MR1988288
Digital Object Identifier: 10.2140/gt.2003.7.311

Subjects:
Primary: 57R67
Secondary: 46L80, 58G10

Rights: Copyright © 2003 Mathematical Sciences Publishers

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