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Valette, Alain

Nom
Valette, Alain
Affiliation principale
Site web
Fonction
Professeur ordinaire
Email
alain.valette@unine.ch
Identifiants
https://libra.unine.ch/handle/123456789/455

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  • Publication
    Métadonnées seulement
    Vanishing and non-vanishing for the first L
    (2005)
    Bourdon, Marc
    ;
    Martin, Florian
    ;
    Valette, Alain 
    We prove two results on the first L-P-cohomology (H) over bar (1)((p))(Gamma) of a finitely generated group Gamma: 1) If N subset of H subset of Gamma is a chain of subgroups, with N non-amenable and normal in Gamma, then (H) over bar (1)((P))(Gamma) = 0 as soon as (H) over bar (1)((P))(H) = 0. This allows for a short proof of a result of W. Luck: if N < Gamma, N is infinite, finitely generated as a group, and Gamma/N contains an element of infinite order, then (H) over bar (1)((2))(Gamma) = 0. 2) If Gamma acts isometrically, properly discontinuously on a proper CAT(- 1) space X, with at least 3 limit points in theta X, then for p larger than the critical exponent e(Gamma) of Gamma in X, one has (H) over bar (1)((p)) not equal A 0. As a consequence we extend a result of Y Shalom: let G be a cocompact lattice in a rank 1 simple Lie group; if G is isomorphic to Gamma, then e(G) < e(Gamma).