Topological Dynamics on Moduli Spaces, I

1999/10/02 by Joseph P. Previte, Previte, Joseph P., Eugene Z. Xia +1 · 1 citation
Mathematics · #11D99 #54H20 #57M05 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:11D99 #msc:54H20 #msc:57M05

paper · pdf · doi:10.48550/arxiv.math/9910008

22 pages, 1 figure in Postscript format

arxiv created 1999/10/07 · arxiv updated 2009/11/30

Abstract

Let M be a one-holed torus with boundary ∂ M (a circle) and Γ the mapping class group of M fixing ∂ 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 ∂ 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)).

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