Topological Dynamics on Moduli Spaces, I

Details Topological Dynamics on Moduli Spaces, I Topological Dynamics on Moduli Spaces, I

1999-10-02

arxiv.org/abs/math/9910008v2

Mathematics

Dynamical Systems

22 pages, 1 figure in Postscript format

Scientific paper

Let M be a one-holed torus with boundary $\partial M$ (a circle) and $\Gamma$ the mapping class group of M fixing $\partial M$. The group $\Gamma$ 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 $\Gamma$-action and give conditions for the individual $\Gamma$-orbits to be dense in ${\mathcal M}_{\mathcal C}(SU(2))$.

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