Mapping Class Group Dynamics on Surface Group Representations

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dc.creatorGoldman, William M.
dc.date2005-09-06
dc.date2006-01-28
dc.date.accessioned2026-07-07T08:10:20Z
dc.date.available2026-07-07T08:10:20Z
dc.descriptionDeformation spaces Hom($π$,G)/G of representations of the fundamental group $π$ of a surface $Σ$ in a Lie group $G$ admit natural actions of the mapping class group $Mod_Σ$, preserving a Poisson structure. When $G$ is compact, the actions are ergodic. In contrast if $G$ is noncompact semisimple, the associated deformation space contains open subsets containing the Fricke-Teichmüller space upon which $Mod_Σ$ acts properly. Properness of the $Mod_Σ$-action relates to (possibly singular) locally homogeneous geometric structures on $Σ$. We summarize known results and state open questions about these actions.
dc.description32 pages, no figures
dc.identifierhttps://arxiv.org/abs/math/0509114
dc.identifierhttp://arxiv.org/abs/math/0509114
dc.identifierProblems on mapping class groups and related topics, 189--214, Proc. Sympos. Pure Math., 74, Amer. Math. Soc., Providence, RI, 2006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/131793
dc.subjectGeometric Topology
dc.subjectDynamical Systems
dc.subject57M50, 58E20
dc.titleMapping Class Group Dynamics on Surface Group Representations
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