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October 2011 Contracting automorphisms and Lp-cohomology in degree one
Yves Cornulier, Romain Tessera
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Ark. Mat. 49(2): 295-324 (October 2011). DOI: 10.1007/s11512-010-0127-z

Abstract

We characterize those Lie groups, and algebraic groups over a local field of characteristic zero, whose first reduced Lp-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.

Funding Statement

The first author was supported by ANR quantiT JCO8_318197.

Citation

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Yves Cornulier. Romain Tessera. "Contracting automorphisms and Lp-cohomology in degree one." Ark. Mat. 49 (2) 295 - 324, October 2011. https://doi.org/10.1007/s11512-010-0127-z

Information

Received: 1 September 2009; Published: October 2011
First available in Project Euclid: 31 January 2017

zbMATH: 1257.22008
MathSciNet: MR2826945
Digital Object Identifier: 10.1007/s11512-010-0127-z

Rights: 2010 © Institut Mittag-Leffler

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Vol.49 • No. 2 • October 2011
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