2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100809We introduce a new technique for finding CAT(-1) surfaces in hyperbolic 3-manifolds. We use this to show that a complete hyperbolic 3-manifold with finitely generated fundamental group is geometrically and topologically tame.60 pages, 7 figures; V3: incorporates referee's suggestions, references updatedGeometric TopologyDifferential Geometrytext