Geometry & Topology
- Geom. Topol.
- Volume 7, Number 1 (2003), 311-319.
On invariants of Hirzebruch and Cheeger–Gromov
We prove that, if is a compact oriented manifold of dimension , where , such that is not torsion-free, then there are infinitely many manifolds that are homotopic equivalent to but not homeomorphic to it. To show the infinite size of the structure set of , we construct a secondary invariant 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.
Geom. Topol., Volume 7, Number 1 (2003), 311-319.
Received: 28 March 2003
Accepted: 30 April 2003
First available in Project Euclid: 21 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57R67: Surgery obstructions, Wall groups [See also 19J25]
Secondary: 46L80: $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22] 58G10
Chang, Stanley; Weinberger, Shmuel. On invariants of Hirzebruch and Cheeger–Gromov. Geom. Topol. 7 (2003), no. 1, 311--319. doi:10.2140/gt.2003.7.311. https://projecteuclid.org/euclid.gt/1513883100