Dick Canary, University of Michigan

Introductory Bumponomics: Deformation Theory of Kleinian Groups

We will survey recent results on the topology of the space AH(M) of all (marked) hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold M. The components of the interior of this space are manifolds and they are enumerated by the set of (marked) homeomorphism types of 3-manifolds homotopy equivalent to M. It has recently been shown that AH(M) is the closure of its interior. However, the global topology of the space AH(M) itself is quite complicated.