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 pi1(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.
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