Proper actions on $\ell ^p$-spaces for relatively hyperbolic groups

Chatterji, Indira; Dahmani, François

doi:10.5802/ahl.26

Proper actions on

ℓ^{p}

-spaces for relatively hyperbolic groups

Chatterji, Indira ¹; Dahmani, François ²

¹ Laboratoire de Mathématiques J.A. Dieudonné UMR 7351 CNRS UNS Université de Nice-Sophia Antipolis 06108 Nice Cedex 02 (France)
² Institut Fourier Université Grenoble Alpes 38000 Grenoble (France)

Annales Henri Lebesgue, Volume 3 (2020), pp. 35-66.

Abstract
Résumé

We show that for any group $G$ that is hyperbolic relative to subgroups that admit a proper affine isometric action on a uniformly convex Banach space, then $G$ acts properly on a uniformly convex Banach space as well.

Nous démontrons que si $G$ est un groupe relativement hyperbolique dont les groupes périphériques peuvent être munis d’actions affines propres sur des espaces de Banach uniformément convexes, alors $G$ lui aussi, peut être muni d’une action propre sur un (autre) espace de Banach uniformément convexe.

Received: 2018-02-27
Revised: 2019-01-28
Accepted: 2019-03-25
Online First: 2020-01-16
Published online: 2020-01-16

DOI: 10.5802/ahl.26

Author's affiliations:

Chatterji, Indira ¹; Dahmani, François ²

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     title = {Proper actions on $\ell ^p$-spaces for relatively hyperbolic groups},
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Chatterji, Indira; Dahmani, François. Proper actions on $\ell ^p$-spaces for relatively hyperbolic groups. Annales Henri Lebesgue, Volume 3 (2020), pp. 35-66. doi : 10.5802/ahl.26. http://archive.numdam.org/articles/10.5802/ahl.26/

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