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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Nicolas Monod 1
@article{CRMATH_2005__340_3_185_0, author = {Nicolas Monod}, 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}, }
Nicolas Monod. Superrigidity for irreducible lattices and geometric splitting. Comptes Rendus. Mathématique, Volume 340 (2005) no. 3, pp. 185-190. doi : 10.1016/j.crma.2004.12.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.12.023/
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