Groups, Geometry, and Dynamics


Full-Text PDF (361 KB) | Metadata | Table of Contents | GGD summary
Volume 9, Issue 2, 2015, pp. 331–368
DOI: 10.4171/GGD/316

Published online: 2015-06-08

Compactification de Thurston d’espaces de réseaux marqués et de l’espace de Torelli

Thomas Haettel[1]

(1) Université de Montpellier, France

We define a compactification of symmetric spaces of noncompact type, seen as spaces of isometry classes of marked lattices, analogous to the Thurston compactification of the Teichmüller space, and we show that it is equivariantly isomorphic to a Satake compactification. We then use it to define a new compactification of the Torelli space of a hyperbolic surface with marked points, and we show that it is equivariantly isomorphic to the Satake compactification of the image of the period mapping. Finally, we describe the natural stratification of a subset of the boundary.

Keywords: Thurston compactification, symmetric space, space of marked lattices, Torelli space, period mapping

Haettel Thomas: Compactification de Thurston d’espaces de réseaux marqués et de l’espace de Torelli. Groups Geom. Dyn. 9 (2015), 331-368. doi: 10.4171/GGD/316