11/4/2004
Dick Canary
University of Michigan and Wesleyen
Deformation theory of hyperbolic 3-manifolds
We will survey recent results concerning the space $AH(M)$ of all hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold $M$. The recent resolution of Thurston's Ending Lamination Conjecture provides a classification of the manifolds in $AH(M)$ in terms of topological data, the marked homeomorphism type of the manifold, and geometric data, which encodes the asymptotic geometry of the ends of the manifold. However, these invariants vary discontinuously over $AH(M)$ and the topology of $AH(M)$ has been found to be much more complicated than expected.