Arkiv för Matematik
- Ark. Mat.
- Volume 49, Number 2 (2011), 295-324.
Contracting automorphisms and Lp-cohomology in degree one
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.
The first author was supported by ANR quantiT JCO8_318197.
Ark. Mat., Volume 49, Number 2 (2011), 295-324.
Received: 1 September 2009
First available in Project Euclid: 31 January 2017
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2010 © Institut Mittag-Leffler
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