[Quelques propriétés des groupes CAT(0)]
Nous présentons des résultats de structure sur les groupes CAT(0), les réseaux CAT(0) et sur les espaces sous-jacents. Nos énoncés reposent notamment sur une étude générale des groupes d'isométries pleins des espaces CAT(0) propres. Nous démontrons des résultats qui généralisent des énoncés classiques sur les variétés de Hadamard et proposons de nouveaux théorèmes d'arithméticité et rigidité.
We announce results on the structure of CAT(0) groups, CAT(0) lattices and of the underlying spaces. Our statements rely notably on a general study of the full isometry groups of proper CAT(0) spaces. Classical statements about Hadamard manifolds are established for singular spaces; new arithmeticity and rigidity statements are obtained.
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@article{CRMATH_2008__346_15-16_857_0,
author = {Caprace, Pierre-Emmanuel and Monod, Nicolas},
title = {Some properties of non-positively curved lattices},
journal = {Comptes Rendus. Math\'ematique},
pages = {857--862},
publisher = {Elsevier},
volume = {346},
number = {15-16},
year = {2008},
doi = {10.1016/j.crma.2008.07.006},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2008.07.006/}
}
TY - JOUR AU - Caprace, Pierre-Emmanuel AU - Monod, Nicolas TI - Some properties of non-positively curved lattices JO - Comptes Rendus. Mathématique PY - 2008 SP - 857 EP - 862 VL - 346 IS - 15-16 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2008.07.006/ DO - 10.1016/j.crma.2008.07.006 LA - en ID - CRMATH_2008__346_15-16_857_0 ER -
%0 Journal Article %A Caprace, Pierre-Emmanuel %A Monod, Nicolas %T Some properties of non-positively curved lattices %J Comptes Rendus. Mathématique %D 2008 %P 857-862 %V 346 %N 15-16 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2008.07.006/ %R 10.1016/j.crma.2008.07.006 %G en %F CRMATH_2008__346_15-16_857_0
Caprace, Pierre-Emmanuel; Monod, Nicolas. Some properties of non-positively curved lattices. Comptes Rendus. Mathématique, Tome 346 (2008) no. 15-16, pp. 857-862. doi : 10.1016/j.crma.2008.07.006. http://www.numdam.org/articles/10.1016/j.crma.2008.07.006/
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