# Geometric Analysis and Topology Seminar

#### Dynamics on Character Varieties for the Free Group

Speaker: Yair Minsky, Yale University

Location: Warren Weaver Hall 512

Date: Thursday, April 8, 2010, 11 a.m.

Synopsis:

The $$\mathrm{SL}(2,C)$$ character variety of a free group $$F_n$$ parametrizes conjugacy classes of representations of $$F_n$$ to the isometry group of hyperbolic 3-space, and hence plays an important role in geometry of hyperbolic 3-manifolds. On the other hand it also has a dynamical aspect, via a natural action by the outer automorphism group of $$F_n$$. We will compare a "geometric decomposition" – in terms of density versus discreteness of the image groups – to a "dynamical decomposition" in terms of proper discontinuity of the automorphism action, and show how they disagree. We will also discuss what is known about ergodicity of the action (joint work with T. Gelander).