Exceptional Discrete Mapping Class Group Orbits in Moduli Spaces

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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.
7 pages, 1 figure

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Dynamical Systems, 54H20; 57M05

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http://salesiana.dossiersoluciones.com/handle/123456789/62012

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0108092
 http://arxiv.org/abs/math/0108092

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arXiv