Topological dynamics on moduli spaces, I

Let M be a one-holed torus with boundary ∂M (a circle) and Γ the mapping class group of M fixing ∂M. The group Γ acts on M_c(SU(2)) which is the space of SU(2)-gauge equivalence classes of flat SU(2)-connections on M with fixed holonomy on ∂M. We study the topological dynamics of the Γ-action and give conditions for the individual Γ-orbits to be dense in M_c(SU(2)).