Mapping Class Group Dynamics on Surface Group Representations
نویسنده
چکیده
Deformation 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 ModΣ, 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 ModΣ acts properly. Properness of the ModΣaction relates to (possibly singular) locally homogeneous geometric structures on Σ. We summarize known results and state open questions about these actions.
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