Exceptional Discrete Mapping Class Group Orbits in Moduli Spaces

2001/08/13 by Joseph P. Previte, Previte, Joseph P., Eugene Z. Xia +1
Mathematics · #54H20 #57M05 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.DS #msc:54H20 #msc:57M05

paper · pdf · doi:10.48550/arxiv.math/0108092

7 pages, 1 figure

arxiv created 2001/08/13 · openalex publication_date 2001/08/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a four-holed sphere and Γ the mapping class group of M fixing ∂ M. The group Γ acts on the space \mathcal M_{\mathcal B}(SU(2)) of SU(2)-gauge equivalence classes of flat SU(2)-connections on M with fixed holonomy on ∂ M. We give examples of flat SU(2)-connections whose holonomy groups are dense in SU(2), but whose Γ-orbits are discrete in \mathcal M_{\mathcal B}(SU(2)). This phenomenon does not occur for surfaces with genus greater than zero.

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