Affiliation:
1. Leonhard Euler International Mathematical Institute Saint Petersburg State University Saint Petersburg Russia
Abstract
AbstractWe 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.
Funder
Ministry of Science and Higher Education of the Russian Federation