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

TL;DR

This paper demonstrates that hyperbolic groups can act properly and affinely on certain quotient spaces of b Banach spaces for all p close to 1, expanding understanding of group actions on Banach spaces.

Contribution

It establishes the existence of proper affine isometric actions of hyperbolic groups on quotient b spaces for p near 1, a new result in geometric group theory.

Findings

Hyperbolic groups admit proper affine actions on quotient b spaces for p close to 1

Extension of known group action results to a broader class of Banach space quotients

Advancement in understanding the geometry of hyperbolic groups and Banach space interactions

Abstract

We prove that any hyperbolic group admits a proper affine isometric action on a quotient space of a $\ell^p$ Banach space, for all $p>1$ sufficiently close to 1.