On Invariants of Hirzebruch and Cheeger{Gromov

By Stanley S. Chang, Shmuel Weinberger. 2003

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We prove that, if M is a compact oriented manifold of dimension 4k +3 , where k> 0, such that 1(M) is not torsion-free, then there are innitely many manifolds that are homotopic equivalent to M but not homeomorphic to it. To show the innite size of the structure set of M ,w e construct a secondary invariant (2) : S(M ) ! R that coincides with the {invariant of Cheeger{Gromov. In particular, our result shows that the {invariant is not a homotopy invariant for the manifolds in question. AMS Classication numbers Primary: 57R67 Secondary: 46L80, 58G10

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d9f47e21c698c4b2a3ed41bbaca6df8968f444ec

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Topological rigidity for non-aspherical manifolds (2005, background): “Then there are infinitely many pairwise not homeomorphic smooth manifolds which are homotopy equivalent to M (and even simply and tangentially homotopy equivalent to M) but not homeomorphic to M.”
Homology cobordism invariants and the Cochran-Orr-Teichner filtration of the link concordance group (2006, background): “r knots (m = 1), the successive quotients of the (n)-solvable ﬁltration are known to be inﬁnite. However, it is unknown, for knots, if these quotients have inﬁnite rank when n ≥ 3. 1. Introduction In [CW], S. Chang and S. Weinberger use a signature defect to deﬁne an invariant of a (4k−1)-dimensiona”