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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Espace des modules marqués des surfaces projectives convexes de volume fini

Ludovic Marquis

Geometry & Topology 14 (2010) 2103–2149
Abstract

Cet article est la suite de l’article [arXiv :0902.3143] dans lequel l’auteur caractérisait le fait d’être de volume fini pour une surface projective convexe. On montre ici que l’espace des modules βf(Σg,p) des structures projectives convexes de volume fini sur la surface βf(Σg,p) de genre g à p pointes est homéomorphe à 16g16+6p.

Enfin, on montre que βf(Σg,p) s’identifie à une composante connexe de l’espace des représentations du groupe fondamental de Σg,p dans SL3(ℝ) qui conservent les paraboliques à conjugaison près.

This article follows the article [arXiv :0902.3143] in which the author characterizes the fact of being of finite volume for a convex projective surface. We show here that the moduli space βf(Σg,p) of convex projective structures on the surface Σg,p of genus g with p punctures is homeomorphic to 16g16+6p.

Finally, we show that βf(Σg,p) can be identified with a connected component of the space of representations of the fundamental group of Σg,p in SL3(ℝ) which keep the parabolics modulo conjugation.

Keywords
convex projective geometry, surface, moduli space
Mathematical Subject Classification 2000
Primary: 57M50, 51M10, 51A05
Secondary: 20F65
References
Publication
Received: 30 October 2009
Revised: 27 August 2010
Accepted: 1 August 2010
Published: 9 October 2010
Proposed: Benson Farb
Seconded: Jean-Pierre Otal, Simon Donaldson
Authors
Ludovic Marquis
Unité de Mathématiques Pures et Appliquées
CNRS UMR 5669
ENS Lyon
46, allée d’Italie
69364 Lyon Cedex 07
France
http://www.umpa.ens-lyon.fr/~lmarquis/