Realising end invariants by limits of minimally parabolic, geometrically finite groups

Details Realising end invariants by limits of minimally parabolic, geometrically finite groups Realising end invariants by limits of minimally parabolic, geometrically finite groups

2005-04-27

arxiv.org/abs/math/0504546v4

Mathematics

Geometric Topology

fourth version: Introduction rewritten; some arguments in Sec. 5 and 6 clarified.

Scientific paper

We shall show that for a given homeomorphism type and a set of end invariants (including the parabolic locus) with necessary topological conditions which a topologically tame Kleinian group with that homeomorphism type must satisfy, there is an algebraic limit of minimally parabolic, geometrically finite Kleinian groups which has exactly that homeomorphism type and end invariants. This shows that the Bers-Sullivan-Thurston density conjecture follows from Marden's conjecture proved by Agol, Calegari-Gabai combined with Thurston's uniformisation theorem and the ending lamination conjecture proved by Minsky, partially collaborating with Masur, Brock and Canary.

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