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arXiv · 2309.07013

Induced quasi-isometries of hyperbolic spaces, Markov chains, and acylindrical hyperbolicity

Antoine Goldsborough·Mark Hagen·Harry Petyt·Jacob Russell·Alessandro Sisto
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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.

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Antoine Goldsborough, Mark Hagen, Harry Petyt, Jacob Russell, Alessandro Sisto. 2023-09-13. Induced quasi-isometries of hyperbolic spaces, Markov chains, and acylindrical hyperbolicity. https://arxiv.org/abs/2309.07013

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