Topological dynamics on moduli spaces II

Let $M$ be an orientable genus $g>0$ surface with boundary $\partial M$. Let $\Gamma$ be the mapping class group of $M$ fixing $\partial M$. The group $\Gamma$ acts on ${\mathcal M}_{\mathcal C} = \operatorname{Hom}_{\mathcal C}(\pi_1(M),\operatorname{SU}(2))/\operatorname{SU}(2),$ the space of $\operatorname{SU}(2)$-gauge equivalence classes of flat $\operatorname{SU}(2)$-connections on $M$ with fixed holonomy on $\partial M$. We study the topological dynamics of the $\Gamma$-action and give conditions for the individual $\Gamma$-orbits to be dense in ${\mathcal M}_{\mathcal C}$.