Arkiv för Matematik

  • Ark. Mat.
  • Volume 49, Number 2 (2011), 295-324.

Contracting automorphisms and Lp-cohomology in degree one

Yves Cornulier and Romain Tessera

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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.

Note

The first author was supported by ANR quantiT JCO8_318197.

Article information

Source
Ark. Mat., Volume 49, Number 2 (2011), 295-324.

Dates
Received: 1 September 2009
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907144

Digital Object Identifier
doi:10.1007/s11512-010-0127-z

Mathematical Reviews number (MathSciNet)
MR2826945

Zentralblatt MATH identifier
1257.22008

Rights
2010 © Institut Mittag-Leffler

Citation

Cornulier, Yves; Tessera, Romain. Contracting automorphisms and L p -cohomology in degree one. Ark. Mat. 49 (2011), no. 2, 295--324. doi:10.1007/s11512-010-0127-z. https://projecteuclid.org/euclid.afm/1485907144


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