Tameness of hyperbolic 3-manifolds

2004/05/29 by Ian Agol, Agol, Ian · 5 citations
Mathematics · #57M50 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.DG #math.GT #msc:57M50

paper · pdf · doi:10.48550/arxiv.math/0405568

22 pages, 1 figure

arxiv created 2004/05/29 · arxiv updated 2009/12/01

Abstract

We show that hyperbolic 3-manifolds with finitely generated fundamental group are tame, that is the ends are products. We actually work in slightly greater generality with pinched negatively curved manifolds with hyperbolic cusps. This answers a conjecture of Marden and implies the Ahlfors measure conjecture. Applications are given to other questions about Kleinian groups and 3-manifolds.

Cited by

• Determining subgroups via stationary measures
• Irreducible groups and ergodicity in the boundary
• Brownian motion and orbit counting of Kleinian groups
• Peripheral subgroups of Kleinian groups
• Bounded volume class and Cheeger isoperimetric constant for negatively curved manifolds

Related

• Marden's Tameness Conjecture: history and applications
• Tameness on the boundary and Ahlfors' measure conjecture
• The PL-methods for hyperbolic 3-manifolds to prove tameness
• Drilling cores of hyperbolic 3-manifolds to prove tameness
• Geometrically infinite surfaces in 3-manifolds with hyperbolic fundamental group