### Domains of Discontinuity for Anosov Representations and Generalized Teichmüller Spaces

**Guichard, O ***(Paris-Sud 11)*

Wednesday 16 March 2011, 10:00-11:00

Satellite

#### Abstract

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.