Induced quasi-isometries of hyperbolic spaces, Markov chains, and acylindrical hyperbolicity (with an appendix by Jacob Russell)

  • Antoine Goldsborough

    Heriot-Watt University, Edinburgh, UK
  • Mark F. Hagen

    University of Bristol, Bristol, UK
  • Harry Petyt

    University of Oxford, Oxford, UK
  • Alessandro Sisto

    Heriot-Watt University, Edinburgh, UK
Induced quasi-isometries of hyperbolic spaces, Markov chains, and acylindrical hyperbolicity (with an appendix by Jacob Russell) cover
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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.

Cite this article

Antoine Goldsborough, Mark F. Hagen, Harry Petyt, Alessandro Sisto, Induced quasi-isometries of hyperbolic spaces, Markov chains, and acylindrical hyperbolicity (with an appendix by Jacob Russell). Groups Geom. Dyn. (2025), published online first

DOI 10.4171/GGD/873