2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98324We prove that simple, thick hyperbolic P-manifolds of dimension >2 exhibit Mostow rigidity. We also prove a quasi-isometry rigidity result for the fundamental groups of simple, thick hyperbolic P-manifolds of dimension >2. The key tool in the proofs of these rigidity results is a strong form of the Jordan separation theorem, for maps from S^n to S^{n+1} which are not necessarily injective.25 pages; shorter proofs of Lemmas 2.4, 2.5, minor typos corrected, added referencesGeometric TopologyDifferential GeometryGroup Theorytext