2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/133115In this survey paper, we outline the proofs of the rigidity results for simple, thick, hyperbolic P-manifolds found in our three earlier papers math.GR/0506518, math.GT/0410476, and math.GR/0409586. We discuss how the arguments change in the two, three, and higher dimensional settings. This paper was written for the 22nd Annual Workshop in Geometric Topology (Colorado Springs, June 2005).11 pages, written for the 22nd Annual Workshop in Geometric TopologyGeometric TopologyDifferential GeometryGroup Theorytext