Maximal Representations of Surface Groups: Symplectic Anosov Structures
Abstract
Let G be a connected semisimple Lie group such that the associated symmetric space X is Hermitian and let Gamma be the fundamental group of a compact orientable surface of genus at least 2. We survey the study of maximal representations, that is the subset of Hom(Gamma,G) which is a union of components characterized by the maximality of the Toledo invariant. Then we concentrate on the particular case G=SP(2n,R), and we show that the image of Gamma under any maximal representation is a discrete faithful realization of Gamma as a Kleinian group of complex motions in X with an associated Anosov system, and whose limit set in an appropriate compactification of X is a rectifiable circle.
Cite
@article{arxiv.math/0506079,
title = {Maximal Representations of Surface Groups: Symplectic Anosov Structures},
author = {Marc Burger and Alessandra Iozzi and Francois Labourie and Anna Wienhard},
journal= {arXiv preprint arXiv:math/0506079},
year = {2007}
}
Comments
50 pages, 4 figures. This replaces a previous version: several typos are corrected and the exposition is improved in several places. The paper will appear in a special issue of the Quarterly Journal of Pure and Applied Mathematics (QJPAM) in honor of Armand Borel (October 2005)