Topological tameness may be viewed as a property of the ends of the manifold, namely, having a local product structure.
The conjecture was raised in the form of a question by Albert Marden, who proved that any geometrically finite hyperbolic 3-manifold is topologically tame.
Partial results had been obtained by Thurston, Brock, Bromberg, Canary, Evans, Minsky, Ohshika.
[citation needed] An important sufficient condition for tameness in terms of splittings of the fundamental group had been obtained by Bonahon.
[citation needed] The conjecture was proved in 2004 by Ian Agol, and independently, by Danny Calegari and David Gabai.