[La courbure strictement négative d'un point de vue cohomologique et superrigidité des cocycles]
Nous proposons de nouvelles méthodes cohomologiques pour établir des énoncés de superrigidité dans le cadre général des espaces métriques à courbure strictement négative. Nos résultats s'appliquent aux réseaux irréductibles, ou plus généralement aux cocycles, pour des produits de groupes localement compacts généraux. Avec le concours d'un nouveau théorème d'annulation, on subsume et généralise de la sorte tous les résultats qui allaient dans ce sens ; en outre, les énoncés de non annulation fournissent une vaste classe d'exemples pour nos résultats en équivalence orbitale (Monod et Shalom, Ann. of Math., in press). Nous donnons une preuve dans le cas particulièrement simple des arbres.
In the framework of general negatively curved spaces, we present new superrigidity results and introduce new techniques based on bounded cohomology. This applies to irreducible lattices, and more generally to cocycles, of products of arbitrary locally compact groups. Together with a new vanishing result for higher rank groups, this also generalizes and unifies all previously known results in that direction. The non-vanishing results provide a large class of examples for our results on orbit equivalence rigidity (Monod and Shalom, Ann. of Math., in press). We prove the ‘toy-case’ of actions on trees.
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@article{CRMATH_2003__337_10_635_0,
author = {Monod, Nicolas and Shalom, Yehuda},
title = {Negative curvature from a cohomological viewpoint and cocycle superrigidity},
journal = {Comptes Rendus. Math\'ematique},
pages = {635--638},
publisher = {Elsevier},
volume = {337},
number = {10},
year = {2003},
doi = {10.1016/j.crma.2003.10.002},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2003.10.002/}
}
TY - JOUR AU - Monod, Nicolas AU - Shalom, Yehuda TI - Negative curvature from a cohomological viewpoint and cocycle superrigidity JO - Comptes Rendus. Mathématique PY - 2003 SP - 635 EP - 638 VL - 337 IS - 10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2003.10.002/ DO - 10.1016/j.crma.2003.10.002 LA - en ID - CRMATH_2003__337_10_635_0 ER -
%0 Journal Article %A Monod, Nicolas %A Shalom, Yehuda %T Negative curvature from a cohomological viewpoint and cocycle superrigidity %J Comptes Rendus. Mathématique %D 2003 %P 635-638 %V 337 %N 10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2003.10.002/ %R 10.1016/j.crma.2003.10.002 %G en %F CRMATH_2003__337_10_635_0
Monod, Nicolas; Shalom, Yehuda. Negative curvature from a cohomological viewpoint and cocycle superrigidity. Comptes Rendus. Mathématique, Tome 337 (2003) no. 10, pp. 635-638. doi : 10.1016/j.crma.2003.10.002. http://www.numdam.org/articles/10.1016/j.crma.2003.10.002/
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