Surface groups, Hermitian symmetric spaces, and the Toledo invariant
by
Anna Wienhard
University of Bonn
Coauthors: Marc Burger and Alessandra Iozzi

The Toledo invariant is a bounded real valued invariant associated to a representations of the fundamental group of a closed Riemann surface into the Lie group of a Hermitian symmetric space, which is explicitly computable. We show that representations having maximal Toledo invariant are faithful with discrete image and satisfy some rigidity property. As a consequence the connected component of the representation variety consisting of such representations provide a meaningful generalization of Teichmüller space. To prove the results we make essential use of methods from bounded cohomology.

Date received: December 4, 2003