Espace de Modules Marques des Surfaces Projectives Convexes de Volume Fini

Details Espace de Modules Marques des Surfaces Projectives Convexes de Volume Fini Espace de Modules Marques des Surfaces Projectives Convexes de Volume Fini

2009-10-30

arxiv.org/abs/0910.5839v1

Geometry & Topology 14 (2010), 2103-2149

Mathematics

Geometric Topology

Scientific paper

This article follow the article {http://hal.archives-ouvertes.fr/hal-00361030/fr/} in which the author characterize the fact of being of finite volume for a convex projective surface. We show here that the moduli space $\beta_f(\Sigma_{g,p})$ of the convex projective structure on the surface $\Sigma_{g,p}$ of genius $g$ with $p$ punctures is homeomorphic to $\R^{16g-16+6p}$. Finally, we show that $\beta_f(\Sigma_{g,p})$ can be identify with a connected component of the space of representation of the fundamental group of $\Sigma_{g,p}$ in $SL(3,R)$ which keep the parabolic modulo conjugaison.

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