On ℎ-cobordisms of spherical space forms

Kwasik, Sławomir; Schultz, Reinhard

doi:10.1090/S0002-9939-99-04637-7

On $h$-cobordisms of spherical space forms
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Proc. Amer. Math. Soc. 127 (1999), 1525-1532 Request permission

Abstract:

Given a manifold $M$ of dimension at least 4 whose universal covering is homeomorphic to a sphere, the main result states that a compact manifold $W$ is isomorphic to a cylinder $M\times [0,1]$ if and only if $W$ is homotopy equivalent to this cylinder and the boundary is isomorphic to two copies of $M$; this holds in the smooth, PL and topological categories. The result yields a classification of smooth, finite group actions on homotopy spheres (in dimensions $\geq 5$) with exactly two singular points.

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