Mapping Class Group Dynamics on Surface Group Representations

  title={Mapping Class Group Dynamics on Surface Group Representations},
  author={William M. Goldman},
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… CONTINUE READING
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