Hyperbolicity and uniformly Lipschitz affine actions on subspaces of $L^1$
Group Theory
2023-10-24 v2 Functional Analysis
Abstract
We show that every hyperbolic group has a proper uniformly Lipschitz affine action on a subspace of an space. We also prove that every acylindrically hyperbolic group has a uniformly Lipschitz affine action on such a space with unbounded orbits. Our main tools are the -bicombings on hyperbolic groups constructed by Mineyev and the characterisation of acylindrical hyperbolicity in terms of actions on quasi-trees by Balasubramanya.
Keywords
Cite
@article{arxiv.2207.14691,
title = {Hyperbolicity and uniformly Lipschitz affine actions on subspaces of $L^1$},
author = {Ignacio Vergara},
journal= {arXiv preprint arXiv:2207.14691},
year = {2023}
}
Comments
Final version, 8 pages. To appear in Bulletin of the London Mathematical Society. There was a conceptual mistake in the previous version. Section 3 has been considerably expanded in order to fix it