Work

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

Year: 2025

Type: article

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.

Source: Groups Geometry and Dynamics

DOI: 10.4171/ggd/873

Authors: Antoine Goldsborough, Mark F. Hagen, Harry Petyt, Alessandro Sisto

Institutions: Heriot-Watt University, University of Bristol, University of Oxford

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4408551994

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