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Domains of Discontinuity for Anosov Representations and Generalized Teichmüller Spaces

Wednesday 16th March 2011 - 10:00 to 11:00
Many representations of surface groups (in particular those belonging to "generalized" Teichmüller spaces) are known to satisfy a strong dynamical property: they are Anosov representations. We shall first explain more fully this notion due to F. Labourie. Secondly we will explain how an Anosov representation $\Gamma \to G$ (for any group $\Gamma$) can be interpreted as the holonomy representation of a geometric structure by constructing a domain of discontinuity with compact quotient for $\Gamma$ into a homogenous $G$-space. At last we shall see to what extent this construction can be used in interpreting the generalized Teichmüller spaces as moduli of geometric structures.

This is a joint work with Anna Wienhard.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons