The authors’ 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”.