Thurston's ending lamination conjecture

Let $M$ be a hyperbolic $3$-manifold with finitely generated fundamental group. Its topological type consists of its underlying topology, and its end invariants encode the geometry of its ends. Thurston's ending lamination conjecture. The manifold $M$ is uniquely determined by its topological type and its end invariants. This conjecture concerns the classification of hyperbolic $3$-manifolds through end data; the source states that its proof, together with the proof of Marden's tameness conjecture, gives a broad picture of hyperbolic $3$-manifolds.