The purpose of this project is to analyze various aspects of hyperbolic structures on 3-dimensional manifolds. Professor Kerckhoff will study the deformation theory of hyperbolic cone manifolds, manifolds with Dehn surgery singularities, and infinite-volume geometrically finite manifolds, using a differential geometric analysis of the relevant Hodge theory. Professor Canary wishes to study the analytic and topological structure of the ends of hyperbolic 3-manifolds and their relation to the deformation theory of Kleinian groups. Three-manifolds are very natural objects of study. We live in one, after all. It is therefore surprising what large gaps remain in our knowledge of them.
