High Quality Content by WIKIPEDIA articles! In mathematics, the tameness conjecture states that every complete hyperbolic 3-manifold with finitely generated fundamental group is "topologically tame", i.e. homeomorphic to the interior of a compact 3-manifold. The conjecture originated with Al Marden. It has been proved in 2004 by Ian Agol and, independently, by Danny Calegari and David Gabai and is now known as the tameness theorem. It is one of the fundamental properties of geometrically infinite hyperbolic 3-manifolds, together with the density conjecture and the ending lamination conjecture, which have also been proved.

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