Abstract:
Abstract. The article develops a system of local holomorphic coordinates for the space of hyperbolic 3--manifolds with the fundamental group of a surface. These coordinates depend on the choice of a geodesic lamination on the surface, and are a complexified version of Thurston's shear coordinates for Teichm uller space. The imaginary part of these coordinates measures the bending of a pleated surface realizing the geodesic lamination. We also show how these coordinates are related, via Thurston symplectic form on the space of measured geodesic laminations, to the complex length function and to its di#erential. R esum e. L'article pr esente un syst eme de coordonn ees locales holomorphes pour l'espace des vari et es hyperboliques de dimension 3 qui ont le groupe fondamental d'une surface. Ces coordonn ees d ependent du choix d'une lamination g eod esique sur la surface, et forment une complexification des coordonn ees de d ecalage introduites par Thurston pour l'espace de Teichm uller. La partie imaginaire de ces coordonn ees mesure la courbure d'une surface pliss ee r ealisant la lamination g eod esique. De plus, nous montrons comment ces coordonn ees sont reli ees, par l'interm ediaire de la forme symplectique de Thurston sur l'espace des laminations g eod esiques mesur ees, a la fonction longueur complexe et a sa di # erentielle.
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