Countable groups are mapping class groups of hyperbolic 3-manifolds

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76338We prove that for every countable group G there exists a hyperbolic 3-manifold M such that the isometry group of M, the mapping class group of M, and the outer automorphism group of the fundamental group of M are isomorphic to G.15 pages, 6 figuresGeometric TopologyGroup Theory57M50 (primary); 20F29, 30F40 (secondary)Countable groups are mapping class groups of hyperbolic 3-manifoldstext