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We define a compactification of symmetric spaces of noncompact type, seen asspaces of isometry classes of marked lattices, analogous to the Thurstoncompactification of the Teichm\"uller space, and we show that it isequivariantly isomorphic to a Satake compactification. We then use it to definea new compactification of the Torelli space of a hyperbolic surface with markedpoints, and we show that it is equivariantly isomorphic to the Satakecompactification of the image of the period mapping. Finally, we describe thenatural stratification of a subset of the boundary.

Compactification de Thurston d'espaces de r\'eseaux marqu\'es et de l'espace de Torelli