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Topological dynamics on moduli spaces II

Authors:	Joseph P Previte Eugene Z Xia

Institution:	School of Science, Penn State University Erie, The Behrend College, Erie, Pennsylvania 16563 ; Department of Mathematics & Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515

Abstract:	Let be an orientable genus surface with boundary $\partial M$ . Let $\Gamma$ be the mapping class group of 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 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 ${\mathcal M}_{\mathcal C}$ .

Keywords:	Fundamental group of a surface mapping class group Dehn twist topological dynamics moduli spaces

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