[La super-rigidité des réseaux irréductibles et un théorème de décomposition]
Nous exposons des résultats de super-rigidité pour les actions de réseaux irréductibles en géométrie de Hadamard, singulière ou non. Une de nos motivations est de présenter une preuve élémentaire du théorème de super-rigidité de Margulis pour les réseaux uniformes dans les groupes algébriques semi-simples (non simples) ; nos méthodes s'appliquent cependant aux réseaux dans des produits de groupes complètement généraux. Notre preuve repose notamment sur un théorème de décomposition qui généralise le théorème de Lawson–Yau/Gromoll–Wolf aux dimensions infinies, ou plus précisément aux espaces complets généraux.
We propose general superrigidity results for actions of irreducible lattices on spaces. In particular, we obtain a new and self-contained proof of Margulis' superrigidity theorem for uniform irreducible lattices in non-simple groups. However, the statements hold for lattices in products of arbitrary groups; likewise, the geometric representations need not be linear. The proof uses notably a new splitting theorem which can be viewed as an infinite-dimensional and singular generalization of the Lawson–Yau/Gromoll–Wolf theorem.
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@article{CRMATH_2005__340_3_185_0,
author = {Monod, Nicolas},
title = {Superrigidity for irreducible lattices and geometric splitting},
journal = {Comptes Rendus. Math\'ematique},
pages = {185--190},
publisher = {Elsevier},
volume = {340},
number = {3},
year = {2005},
doi = {10.1016/j.crma.2004.12.023},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.12.023/}
}
TY - JOUR AU - Monod, Nicolas TI - Superrigidity for irreducible lattices and geometric splitting JO - Comptes Rendus. Mathématique PY - 2005 SP - 185 EP - 190 VL - 340 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.12.023/ DO - 10.1016/j.crma.2004.12.023 LA - en ID - CRMATH_2005__340_3_185_0 ER -
%0 Journal Article %A Monod, Nicolas %T Superrigidity for irreducible lattices and geometric splitting %J Comptes Rendus. Mathématique %D 2005 %P 185-190 %V 340 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.12.023/ %R 10.1016/j.crma.2004.12.023 %G en %F CRMATH_2005__340_3_185_0
Monod, Nicolas. Superrigidity for irreducible lattices and geometric splitting. Comptes Rendus. Mathématique, Tome 340 (2005) no. 3, pp. 185-190. doi : 10.1016/j.crma.2004.12.023. http://www.numdam.org/articles/10.1016/j.crma.2004.12.023/
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