Topological Dynamics on Moduli Spaces II

Details Topological Dynamics on Moduli Spaces II Topological Dynamics on Moduli Spaces II

1999-10-06

arxiv.org/abs/math/9910036v2

Mathematics

Dynamical Systems

39 pages, 12 figures

Scientific paper

Let M be a Riemann surface with boundary $\partial M$ and genus greater than zero. Let $\Gamma$ be the mapping class group of M fixing $\partial M$. The group $\Gamma$ acts on ${\mathcal M}_{\mathcal C} = \Hom_{\mathcal C}(\pi_1(M),SU(2)/SU(2)$ 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 $\Gamma$-action and give conditions for the individual $\Gamma$-orbits to be dense in ${\mathcal M}_{\mathcal C}$.

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