Maximal Representations of Surface Groups: Symplectic Anosov Structures
نویسنده
چکیده
Let G be a connected semisimple Lie group such that the associated symmetric space X is Hermitian and let Γg be the fundamental group of a compact orientable surface of genus g ≥ 2. We survey the study of maximal representations of Γg into G that is the subset of Hom(Γg, G) which is a union of components characterized by the maximality of the Toledo invariant ([16] and [14]). Then we concentrate on the particular case G = Sp(2n,R), and we show that if ρ is any maximal representation then the image ρ(Γg) is a discrete, faithful realizations of Γg 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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