Compactification de Thurston d’espaces de réseaux marqués et de l’espace de Torelli
Groups, geometry, and dynamics, Tome 9 (2015) no. 2, pp. 331-368
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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.
Classification :
32-XX, 53-XX
Mots-clés : Thurston compactification, symmetric space, space of marked lattices, Torelli space, period mapping
Mots-clés : Thurston compactification, symmetric space, space of marked lattices, Torelli space, period mapping
Affiliations des auteurs :
Thomas Haettel 1
Thomas Haettel. Compactification de Thurston d’espaces de réseaux marqués et de l’espace de Torelli. Groups, geometry, and dynamics, Tome 9 (2015) no. 2, pp. 331-368. doi: 10.4171/ggd/316
@article{10_4171_ggd_316,
author = {Thomas Haettel},
title = {Compactification de {Thurston} d{\textquoteright}espaces de r\'eseaux marqu\'es et de l{\textquoteright}espace de {Torelli}},
journal = {Groups, geometry, and dynamics},
pages = {331--368},
year = {2015},
volume = {9},
number = {2},
doi = {10.4171/ggd/316},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/316/}
}
TY - JOUR AU - Thomas Haettel TI - Compactification de Thurston d’espaces de réseaux marqués et de l’espace de Torelli JO - Groups, geometry, and dynamics PY - 2015 SP - 331 EP - 368 VL - 9 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/316/ DO - 10.4171/ggd/316 ID - 10_4171_ggd_316 ER -
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