2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122764We prove a topological rigidity result for simple, thick, hyperbolic P-manifolds of dimension 2: isomorphism of the fundamental groups implies homeomorphism of the P-manifolds. An immediate application is a diagram rigidity theorem for certain amalgamations of free groups: the direct limits of two such diagrams are isomorphic if and only if there is an isomorphism between the respective diagrams.16 pagesGroup TheoryGeometric Topologytext