Richard Brown (American University)

The dynamics of surface diffeomorphisms on geometric structure.

Abstract. It is known that for S a compact surface, the modular group (i.e., the mapping class group when S is closed) of S acts symplectically on the symplectic leaves of the Poisson space of SU(2)-characters of representations of the fundamental group of S. Recently, it was established that this action is ergodic with respect to symplectic measure on these leaves. We discuss the dynamics of the actions of individual mapping classes on these character varieties, both explicitly for low genus surfaces, and implicitly for S a high genus surface.