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On h-Cobordisms of Spherical Space Forms

Proceedings of the American Mathematical Society / v.127 no.5. 1999, pp.1525-1532

Author : Kwasik, Slawomir ; Schultz, Reinhard

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.

Keyword : Primary 57R80, 57S25

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