Topology Seminar: Convergence of freely decomposable Kleinian groups

Seminar | September 23 | 4:10-5 p.m. | 3 Evans Hall

 Inkang Kim, KIAS

 Department of Mathematics

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.