Topological Dynamics on Moduli Spaces II

Abstract

Let M be a Riemann surface with boundary $\partial M$ and genus greater than zero. Let $Γ$ be the mapping class group of M fixing $\partial M$. The group $Γ$ acts on ${\mathcal M}_{\mathcal C} = \Hom_{\mathcal C}(π_1(M),SU(2)/SU(2)$ which is the space of SU(2)-gauge equivalence classes of flat SU(2)-connections on M with fixed holonomy on $\partial M$. We study the topological dynamics of the $Γ$-action and give conditions for the individual $Γ$-orbits to be dense in ${\mathcal M}_{\mathcal C}$.