Maximal Representations of Surface Groups: Symplectic Anosov Structures

Details Maximal Representations of Surface Groups: Symplectic Anosov Structures Maximal Representations of Surface Groups: Symplectic Anosov Structures

2005-06-04

arxiv.org/abs/math/0506079v2

Mathematics

Differential Geometry

50 pages, 4 figures. This replaces a previous version: several typos are corrected and the exposition is improved in several p

Scientific paper

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.

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