On ℎ-cobordisms of spherical space forms

Abstract

Given a manifold M M of dimension at least 4 whose universal covering is homeomorphic to a sphere, the main result states that a compact manifold W W is isomorphic to a cylinder M × [ 0 , 1 ] M\times [0,1] if and only if W W is homotopy equivalent to this cylinder and the boundary is isomorphic to two copies of M 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 ≥ 5 \geq 5 ) with exactly two singular points.