MAPPING CLASS GROUP DYNAMICS ON SURFACE GROUP REPRESENTATIONS

By William M. Goldman. 2005

72 citations recorded by the source corpus.

Deformation spaces Hom(�,G)/G of representations of the fundamental groupof a surfacein a Lie group G ad- mit natural actions of the mapping class group Mod�, preserving a Poisson structure. When G is compact, the actions are ergodic. In contrast if G is noncompact semisimple, the associated deforma- tion space contains open subsets containing the Fricke-Teichmuller space upon which Modacts properly. Properness of the Mod�- action relates to (possibly singular) locally homogeneous geomet- ric structures on �. We summarize known results and state open questions about these actions.

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Citations in the corpus

• Quasi-Poisson structures on representation spaces of surfaces (2012, unknown): “It was described in [FR] in terms of ciliated fat graphs and in [GHJW] in terms of group systems, see also [AMM], [La] and the surveys [Au], [Go3], [Hu].”