Topological dynamics on moduli spaces II

Abstract

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 ${\mathcal M}_{\mathcal C} = \operatorname {Hom}_{\mathcal C}(\pi _1(M),\operatorname {SU})/\operatorname {SU},$ the space of $\operatorname {SU}$-gauge equivalence classes of flat $\operatorname {SU}$-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 ${\mathcal M}_{\mathcal C}$.