Induced quasi-isometries of hyperbolic spaces, Markov chains, and acylindrical hyperbolicity
Group Theory
2025-01-08 v2 Probability
Abstract
We show that quasi-isometries of (well-behaved) hierarchically hyperbolic groups descend to quasi-isometries of their maximal hyperbolic space. This has two applications, one relating to quasi-isometry invariance of acylindrical hyperbolicity, and the other a linear progress result for Markov chains. The appendix, by Jacob Russell, contains a partial converse under the (necessary) condition that the maximal hyperbolic space is one-ended.
Keywords
Cite
@article{arxiv.2309.07013,
title = {Induced quasi-isometries of hyperbolic spaces, Markov chains, and acylindrical hyperbolicity},
author = {Antoine Goldsborough and Mark Hagen and Harry Petyt and Jacob Russell and Alessandro Sisto},
journal= {arXiv preprint arXiv:2309.07013},
year = {2025}
}
Comments
38 pages, 1 figure. Main paper by A. Goldsborough, M. Hagen, H. Petyt and A. Sisto; appendix by J. Russell. To appear in Groups, Geometry, and Dynamics