Groups that (do not) act isometrically on hyperbolic spaces
Group Theory
2025-08-19 v2
Abstract
In this paper, we show that if a group acts isometrically on a good hyperbolic space of finite volume entropy through a non-elementary action, then it admits an affine action on some -space with an unbounded orbit for sufficiently large . As an application, we prove that any isometric action of a group with the fixed point property on a good hyperbolic space must have a bounded orbit.
Cite
@article{arxiv.2212.12837,
title = {Groups that (do not) act isometrically on hyperbolic spaces},
author = {Yanlong Hao},
journal= {arXiv preprint arXiv:2212.12837},
year = {2025}
}
Comments
12 pages. arXiv admin note: text overlap with arXiv:1202.2597, arXiv:1404.0903 by other authors