2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/226137We prove that an integral homology 3-sphere is S^3 if and only if it admits four periodic diffeomorphisms of odd prime orders whose space of orbits is S^3. As an application we show that an irreducible integral homology sphere which is not S^3 is the cyclic branched cover of odd prime order of at most four knots in S^3. A result on the structure of finite groups of odd order acting on integral homology spheres is also obtained.This is the version published by Geometry & Topology Monographs on 29 April 2008Geometric Topology57M40, 57M12, 57M50, 57M60, 57S17text