Hyperbolic manifolds and Mostow Rigidity

By Maxime Fortier Bourque

September 21, 2011

Abstract

The geometrization theorem states that closed 3-manifolds can be cut into pieces each admitting one of 8 geometric structures. In some sense "most" possible pieces have a hyperbolic structure, so it is good to understand hyperbolic manifolds. One of the first important results about closed hyperbolic 3-manifolds is that they are determined up to isometry by their fundamental group. This is called Mostow's Rigidity Theorem and the goal of this talk is to understand its statement.