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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References

SHOWING 1-10 OF 50 REFERENCES
Sur Les Groupes Hyperboliques D'Apres Mikhael Gromov
- Qa faut avouer, dit Trouscaillon qui, dans cette simple ellipse, utilisait hyperboliquement Ie cercle vicieux de la parabole. - Bun, dit Ie Sanctimontronais, j'y vais. (R. Queneau, Zazie dans IeExpand
Métriques de Carnot-Carthéodory et quasiisométries des espaces symétriques de rang un
We exhibit a rigidity property of the simple groups Sp(n, 1) and F7-20 which implies Mostow rigidity. This property does not extend to O(n, 1) and U(n, 1). The proof relies on quasiconformal theoryExpand
1-cohomologie des représentations unitaires des groupes de Lie semi-simples et résolubles. Produits tensoriels continus de représentations
© Bulletin de la S. M. F., 1977, tous droits réservés. L’accès aux archives de la revue « Bulletin de la S. M. F. » (http: //smf.emath.fr/Publications/Bulletin/Presentation.html) implique l’accordExpand
Croissance polynomiale et périodes des fonctions harmoniques
© Bulletin de la S. M. F., 1973, tous droits réservés. L’accès aux archives de la revue « Bulletin de la S. M. F. » (http://smf. emath.fr/Publications/Bulletin/Presentation.html) implique l’accordExpand
Large scale Sobolev inequalities on metric measure spaces and applications
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Harmonic functions on graphs and on other discrete structures are interesting not only for their own sake but also because they are closely related to harmonic functions on noncompact RiemannianExpand
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