TOPOLOGY SEMINAR

2/16/2006

Anna Wienhard
Institute for Advanced Study

Generalizations of Teichmueller space in the Hermitian context

The Teichmueller space of a closed oriented surface S parametrizes all hyperbolic structures on S. Associating with a hyperbolic structure its holonomy representation embeds the Teichmueller space as one connected component into the space of all representation of the fundamental group G of S into PSL(2,R). We will show that the representation variety of representation of G into Lie groups of Hermitian type contains connected components which in many aspects resemble the classical Teichmueller space. There are several interesting links with higher Teichmueller spaces defined by Hitchin in the context of split real Lie groups. (This is joint work with M. Burger and A. Iozzi)