Groups and Dynamics Seminar

Thurston's Hyperbolic Dehn Filling Theorem is a seminal result in the theory of 3-manifolds. Given a single non-compact finite-volume hyperbolic 3-manifold M, the theorem provides a construction for a currently infinite family of closed hyperbolic 3-manifolds converging to M in a geometric sense. The theorem is a major source of examples of 3-manifolds admitting hyperbolic structures, and closely connect the topology of a 3 manifold to the analysis of the PSL(2,C) character variety of its fundamental group. In this talk, we discuss some analogs and generalizations of how our results provide a way to construct new examples of Anosov and relatively Anosov with Jeff Danciger, which applies our results towards exotic new examples of convex cocopact and geometrically finite groups acting on complex hyperbolic 3-space.