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

• 成果类型: Article
• 署名作者: Brock, Jeffrey F.; Canary, Richard D.; Minsky, Yair N.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/anna1s.2012.176.1.1
• 发表日期: 2012
• 页码: 1-149
• 关键词: hyperbolic 3-manifolds; deformation spaces; geometry; complex; LIMITS; homeomorphisms; BOUNDARIES; MANIFOLDS; RIGIDITY; density

摘要

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 a uniformly bilipschitz model for the quotient of H-3 by a Kleinian surface group.