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arXiv · 0708.3266

Convergence of freely decomposable Kleinian groups

Inkang Kim·Cyril Lecuire·Ken'ichi Ohshika
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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.

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Inkang Kim, Cyril Lecuire, Ken'ichi Ohshika. 2011-11-25. Convergence of freely decomposable Kleinian groups. https://arxiv.org/abs/0708.3266

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