On the density of geometrically finite Kleinian groups

2002/12/13 by Jeffrey Brock, Jeffrey F. Brock, Brock, Jeffrey F. +3 · 2 citations
Mathematics · #30F60 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Primary 30F40 #Secondary 37F30 #math.DS #math.GT #msc:30F40 #msc:30F60 #msc:37F30

paper · pdf · doi:10.48550/arxiv.math/0212189

59 pages, 2 figures

arxiv created 2002/12/13 · openalex publication_date 2002/12/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The density conjecture of Bers, Sullivan and Thurston predicts that each complete hyperbolic 3-manifold M with finitely generated fundamental group is an algebraic limit of geometrically finite hyperbolic 3-manifolds. We prove that the conjecture obtains for each complete hyperbolic 3-manifold with no cusps and incompressible ends.

Citations

• Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle
• Minimal stretch maps between hyperbolic surfaces
• Hyperbolic Structures on 3-manifolds, III: Deformations of 3-manifolds with incompressible boundary

Cited by

• Expansion joints in hyperbolic manifolds
• Matrix entries, unipotents, and linearity of amalgams

Related

• Cone-manifolds and the density conjecture
• Tameness on the boundary and Ahlfors' measure conjecture
• Combinatorial and Geometrical Aspects of Hyperbolic 3-Manifolds
• Cores of hyperbolic 3-manifolds and limits of Kleinian groups II
• Hyperbolic Dehn surgery on geometrically infinite 3-manifolds