Actions affines isom\'etriques propres des groupes hyperboliques sur des espaces $\ell^{p}$

TL;DR

This paper provides a straightforward proof that hyperbolic groups can act properly and affinely on large enough $\, ext{ell}^p$-spaces, extending understanding of their geometric actions.

Contribution

It offers a simpler proof of a known result that hyperbolic groups admit proper affine isometric actions on $\, ext{ell}^p$-spaces for sufficiently large p.

Findings

Hyperbolic groups act properly on $\, ext{ell}^p$-spaces for large p

The proof simplifies previous approaches by Yu

Supports the geometric group theory framework

Abstract

We give a simple and relatively short proof of the following fact: any hyperbolic group admits a proper affine isometric action on a $\ell^p$-space for $p$ large enough. A first proof of this result was given by Guoliang Yu.