Espace de Modules Marques des Surfaces Projectives Convexes de Volume Fini

Abstract

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 ${\mathbb{R}}^{16g-16+6p}$. 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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