On Invariants of Hirzebruch and Cheeger-Gromov

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.

Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper9.abs.html

References in corpus (1)

• Various L2-signatures and a topological L2-signature theorem

Cited by in corpus (7)

• Novikov's Conjecture
• Homology Cobordism Invariants and the Cochran-Orr-Teichner Filtration of the Link Concordance Group
• Groups with torsion, bordism and rho-invariants
• Symmetric chain complexes, twisted Blanchfield pairings, and knot concordance
• Grope metrics on the knot concordance set
• Amenable signatures, algebraic solutions, and filtrations of the knot concordance group
• L^2 rho form for normal coverings of fibre bundles