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

Details Compactification de Thurston d'espaces de réseaux marqués et de l'espace de Torelli Compactification de Thurston d'espaces de réseaux marqués et de l'espace de Torelli

2011-04-18

arxiv.org/abs/1104.3417v2

Mathematics

Geometric Topology

In french, 35 pages

Scientific paper

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 Teichm\"uller 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.

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