THE CLASSIFICATION OF KLEINIAN SURFACE GROUPS, II: THE ENDING LAMINATION CONJECTURE

Thurston’s Ending Lamination Conjecture states that a hyperbolic 3manifold N with nitely generated fundamental group is uniquely determined by its topological type and its end invariants. In this paper we prove this conjecture for Kleinian surface groups; the general case when N has incompressible ends relative to its cusps follows readily. The main ingredient is a uniformly bilipschitz model for the quotient of H 3 by a Kleinian surface group.

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