Convergence of freely decomposable Kleinian groups
Geometric Topology
2011-11-28 v2
Abstract
We consider a compact orientable hyperbolic 3-manifold with a compressible boundary. Suppose that we are given a sequence of geometrically finite hyperbolic metrics whose conformal boundary structures at infinity diverge to a projective lamination. We prove that if this limit projective lamination is doubly incompressible, then the sequence has compact closure in the deformation space. As a consequence we generalise Thurston's double limit theorem and solve his conjecture on convergence of function groups affirmatively.
Cite
@article{arxiv.0708.3266,
title = {Convergence of freely decomposable Kleinian groups},
author = {Inkang Kim and Cyril Lecuire and Ken'ichi Ohshika},
journal= {arXiv preprint arXiv:0708.3266},
year = {2011}
}
Comments
Version 2: revised to make it more readable