Maximal Representations of Surface Groups: Symplectic Anosov Structures

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dc.creatorBurger, Marc
dc.creatorIozzi, Alessandra
dc.creatorLabourie, Francois
dc.creatorWienhard, Anna
dc.date2005-06-04
dc.date2005-10-07
dc.date.accessioned2026-07-07T06:40:11Z
dc.date.available2026-07-07T06:40:11Z
dc.descriptionLet 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.
dc.description50 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)
dc.identifierhttps://arxiv.org/abs/math/0506079
dc.identifierhttp://arxiv.org/abs/math/0506079
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/101330
dc.subjectDifferential Geometry
dc.subjectDynamical Systems
dc.titleMaximal Representations of Surface Groups: Symplectic Anosov Structures
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