Topological Dynamics on Moduli Spaces, I

Abstract

Let M be a one-holed torus with boundary $\partial M$ (a circle) and $Γ$ the mapping class group of M fixing $\partial M$. The group $Γ$ acts on ${\mathcal M}_{\mathcal C}(SU(2))$ 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 ${\mathcal M}_{\mathcal C}(SU(2))$.