On Invariants of Hirzebruch and Cheeger-Gromov
Geometric Topology
2014-11-11 v1 Algebraic Topology
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
Cite
@article{arxiv.math/0306247,
title = {On Invariants of Hirzebruch and Cheeger-Gromov},
author = {Stanley Chang and Shmuel Weinberger},
journal= {arXiv preprint arXiv:math/0306247},
year = {2014}
}
Comments
Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper9.abs.html