Phil Huling of SLU to Give April 23rd Talk

Homeomorphic topological spaces have isomorphic fundamental groups. An obvious questionc is then: when must spaces with isomorphic fundamental groups be homeomorphic? That is, when is the fundamental group a complete invariant? Flat conformal deformation theory investigates this question in the case of hyperbolic orbifolds and further asks if we can describe what happens when the fundamental group fails to be a complete invariant. We will look at what is known about these questions and then we will discuss my recent work with cofinite Coxeter groups and the lattices that contain them. In particular, we are able to develop tools which give the deformation spaces of the reflective Bianchi groups.