Anosov Flows, Surface Groups and Curves in Projective Space
Abstract
In 1990, Hitchin's proved a component of the space of representations of a surface group in SL(n,R) is homeomorphic to a ball. For n=2,3 this component has been identified with the holonomies of geometric structures (hyperbolic for n=2, or real projective for n=3). In the preprint "Anosov flows, Surface groups and Curves in Projective Space", we extend this interpretation to higher dimension and show every representation in Hitchin's component is attached to a (special) curve in projective space, thus giving a geometric interpretation of these representations. We also prove these representations are faithful, discrete and purely loxodromic (or hyperbolic)
Cite
@article{arxiv.math/0401230,
title = {Anosov Flows, Surface Groups and Curves in Projective Space},
author = {Francois Labourie},
journal= {arXiv preprint arXiv:math/0401230},
year = {2007}
}
Comments
v2 : in Theorem 1.5, the fact that the action of the mapping classgroup is proper is postponed to another paper. Theorem 4.3. has been replaced by an improvement due to O. Guichard. Various typos are corrected