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Exceptional Discrete Mapping Class Group Orbits in Moduli Spaces

Joseph P. Previte·Eugene Z. Xia
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Abstract

Let $M$ be a four-holed sphere and $Γ$ the mapping class group of $M$ fixing $\partial M$. 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 $\partial M$. 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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Joseph P. Previte, Eugene Z. Xia. 2001-08-13. Exceptional Discrete Mapping Class Group Orbits in Moduli Spaces. https://arxiv.org/abs/math/0108092

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