The classification of Kleinian surface groups, II: The Ending Lamination Conjecture

Jeffrey F. Brock; Richard D. Canary; Yair N. Minsky

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The classification of Kleinian surface groups, II: The Ending Lamination Conjecture

Jeffrey F. Brock·Richard D. Canary·Yair N. Minsky

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Abstract

Thurston's Ending Lamination Conjecture states that a hyperbolic 3-manifold N with finitely 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 the establishment of a uniformly bilipschitz model for a Kleinian surface group. The first half of the proof appeared in math.GT/0302208, and a subsequent paper will establish the Ending Lamination Conjecture in general.

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Jeffrey F. Brock, Richard D. Canary, Yair N. Minsky. 2004-12-01. The classification of Kleinian surface groups, II: The Ending Lamination Conjecture. https://arxiv.org/abs/math/0412006

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