Ending lamination theorem

In hyperbolic geometry, the ending lamination theorem, originally conjectured by William Thurston (1982) as the eleventh problem out of his twenty-four questions, states that hyperbolic 3-manifolds with finitely generated fundamental groups are determined by their topology together with certain "end invariants", which are geodesic laminations on some surfaces in the boundary of the manifold. The ending lamination theorem is a generalization of the Mostow rigidity theorem to hyperbolic manifolds of infinite volume.

Source: Wikipedia — Ending lamination theorem (CC BY-SA 4.0)