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

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.

143 pages. Comprehensive revision and inclusion of the incompressible ends case

References in corpus (2)

• Tameness of hyperbolic 3-manifolds
• Train tracks and the Gromov boundary of the complex of curves

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