On the density of geometrically finite Kleinian groups

By Jeffrey F. Brock, K. Bromberg. 2002

103 citations recorded by the source corpus.

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 3manifold with no cusps and incompressible ends.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/00c70bb667a9830d719e3ebb88519282c7ea4957

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

THE CLASSIFICATION OF KLEINIAN SURFACE GROUPS, II: THE ENDING LAMINATION CONJECTURE (2004, methodology): “Bromberg [19] and Brock-Bromberg [17] previously showed that each representation ρ whose image contains no parabolic elements and for which Nρ has incompressible ends is an algebraic limit of geometrically finite representations, using cone-manifold techniques and the bounded-geometry version of the”
Homotopy equivalences of 3-manifolds and deformation theory of Kleinian groups (2004, background): “2Bromberg [25] and Brock-Bromberg [22] proved that if M has incompressible boundary, ρ ∈ AH(π1(M)), and ρ(π1(M)) contains no maximal cyclic parabolic subgroups, then ρ lies in the closure of GF(π1(M)).”
Realising end invariants by limits of minimally parabolic, geometrically finite groups (2005, methodology): “This result is then generalised to freely indecomposable Kleinian groups in Brock-Bromberg [11].”