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

By Jeffrey F. Brock, Richard Canary, Yair N. Minsky. 2004

313 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/26a2c0c4358bc29c450a5668afc4cc1005785fc6

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Quasiconvexity in the curve complex (2003, background): “Cannon. This fact has applications to the study of mapping class groups and hyperbolic 3-manifolds [7, 9, 2 ]. See also Bowditch [1] for a new and more concrete proof of the hyperbolicity theorem.”
The classification of Kleinian surface groups I : Models and bounds : preprint (2003, methodology): “In the second paper, with Brock and Canary [17], this map will be promoted to a bilipschitz homeomorphism.”
On hyperbolicity of free splitting and free factor complexes (2012, unknown): “Hyperbolicity of the curve complex was an important ingredient in the solution by Masur, Minsky, Brock and Canary of the Ending Lamination Conjecture [21, 25, 9] (see [24] for detailed background discussion about this solution).”
Tameness of hyperbolic 3-manifolds (2004, background): “last year for tame manifolds by Brock, Canary and Minsky (with major contributions from Masur-Minsky) [50, 47, 49, 43, 44, 48, 16 ].”
The Mapping Class Group from the Viewpoint of Measure Equivalence Theory (2005, background): “(This discovery plays an important role in the study of ends of hyperbolic 3-manifolds by Minsky and his collaborators, culminating in the proof of the ending lamination conjecture [11].”