Moduli of Geometric Structures and Representations

4:00 pm Thursday, February 4, 2010
Olivier Guichard (Université Paris-Sud and IAS)

Teichmuller space has well known and less well known descriptions: as the moduli space of hyperbolic structures on a given surface, or as the moduli space of complex structures, or as a special connected component in the space of representations of a surface group into PSL(2, C). Elaborating on this we will describe some spaces of representations of a surface group into other Lie groups (now commonly called "higher Teichmuller spaces"). We will emphasize similarities (faithfulness and discretness of the representations, properness of the action of the mapping class group MCG) as well as differences (existence of integral representations, action of MCG of infinite covolume) with the "classical" Teichmuller space. As a final result we will give a procedure to realize those "higher Teichmuller spaces" as a connected component in a moduli space of geometric structures.


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