Convergence of freely decomposable Kleinian groups

Inkang Kim (1) , Cyril Lecuire (2) , Ken'Ichi Ohshika

1 KIAS - School of Mathematics
2 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Domaines: Topologie géométrique [math.GT]

Inkang Kim, Cyril Lecuire, Ken'Ichi Ohshika. Convergence of freely decomposable Kleinian groups. Inventiones Mathematicae, 2016, 204 (1). ⟨hal-00952735⟩