Topological Dynamics on Moduli Spaces II

1999/10/06 by Joseph P. Previte, Previte, Joseph P., Eugene Z. Xia +1 · 1 citation
Mathematics · #54H20 #57M05 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DS #msc:54H20 #msc:57M05

paper · pdf · doi:10.48550/arxiv.math/9910036

39 pages, 12 figures

arxiv created 1999/10/06 · openalex publication_date 1999/10/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a Riemann surface with boundary ∂ M and genus greater than zero. Let Γ be the mapping class group of M fixing ∂ M. The group Γ acts on \mathcal M_{\mathcal C} = \Hom_{\mathcal C}(π₁(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 ∂ 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}.

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