Compactification de Chabauty des Espaces Symétriques de Type Non Compact
Journal of Lie Theory, Tome 20 (2010) no. 3, pp. 437-468
Voir la notice de l'article provenant de la source Heldermann Verlag
The space of closed subgroups of a locally compact topological group is endowed with a natural topology, called the Chabauty topology. Let X be a symmetric space of noncompact type, and G be its group of isometries. The space X identifies with the subspace of maximal compact subgroups of G : taking the closure gives rise to the Chabauty compactification of the symmetric space X. Using simpler arguments than those presented by Y. Guivarc'h, L. Ji and J. C. Taylor [Compactifications of symmetric spaces, Progr. Math. 156 (1998)] we describe the subgroups that appear in the boundary of the compactification, and classify the maximal distal and maximal amenable subgroups of G. We also provide a straightforward identification between the Chabauty compactification and the polyhedral compactification.
Classification :
57S05, 57S20, 57S25
Mots-clés : Compactification, Chabauty, symmetric space, space of subgroup
Mots-clés : Compactification, Chabauty, symmetric space, space of subgroup
Affiliations des auteurs :
Thomas Haettel 1
Thomas Haettel. Compactification de Chabauty des Espaces Symétriques de Type Non Compact. Journal of Lie Theory, Tome 20 (2010) no. 3, pp. 437-468. http://geodesic.mathdoc.fr/item/JOLT_2010_20_3_a1/
@article{JOLT_2010_20_3_a1,
author = {Thomas Haettel},
title = {Compactification de {Chabauty} des {Espaces} {Sym\'etriques} de {Type} {Non} {Compact}},
journal = {Journal of Lie Theory},
pages = {437--468},
year = {2010},
volume = {20},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2010_20_3_a1/}
}