# Vanishing of the first reduced cohomology with values in an $L^p$-representation

@article{Tessera2006VanishingOT,
title={Vanishing of the first reduced cohomology with values in an \$L^p\$-representation},
author={Romain Tessera},
journal={Annales de l'Institut Fourier},
year={2006},
volume={59},
pages={851-876}
}
• R. Tessera
• Published 31 October 2006
• Mathematics
• Annales de l'Institut Fourier
Nous prouvons que pour une classe de groupes moyennables, incluant tous les groupes moyennables de Lie connexes, la cohomologie reduite en degre 1 a valeurs dans une representation melangeante sur un espace L p , pour p > 1, est nulle. En particulier, cela demontre pour cette classe de groupes moyennables une conjecture de Gromov s'appliquant a tous les groupes de type fini moyennables. Nous obtenons egalement la version "de Lie" de cette conjecture, qui avait ete formulee par Pansu. Nous… Expand
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