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Article Dans Une Revue Arkiv för Matematik Année : 2011

Contracting automorphisms and $L^p$-cohomology in degree one

Résumé

We characterize those Lie groups, and algebraic groups over a local field of characteristic zero, whose first reduced $L^p$-cohomology is zero for all $p>1$, extending a result of Pansu. As an application, we obtain a description of Gromov-hyperbolic groups among those groups. In particular we prove that any non-elementary Gromov-hyperbolic algebraic group over a non-Archimedean local field of zero characteristic is quasi-isometric to a 3-regular tree. We also extend the study to general semidirect products of a locally compact group by a cyclic group acting by contracting automorphisms.

Dates et versions

hal-00832276 , version 1 (10-06-2013)

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Yves de Cornulier, Romain Tessera. Contracting automorphisms and $L^p$-cohomology in degree one. Arkiv för Matematik, 2011, 49 (2), pp.295-324. ⟨10.1007/s11512-010-0127-z⟩. ⟨hal-00832276⟩
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