Generalised Baumslag–Solitar groups and hierarchically hyperbolic groups

Button, Jack O

doi:10.2140/agt.2025.25.2253

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ISSN (electronic): 1472-2739

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Generalised Baumslag–Solitar groups and hierarchically hyperbolic groups

Jack O Button

Algebraic & Geometric Topology 25 (2025) 2253–2279

DOI: 10.2140/agt.2025.25.2253

Abstract

We look at isometric actions on arbitrary hyperbolic spaces of generalised Baumslag–Solitar groups of any rank (the rank of the free abelian vertex and edge subgroups). It is known that being a hierarchically hyperbolic group is not a quasiisometric invariant. We show that virtually being a hierarchically hyperbolic group is not invariant under quasiisometry either, and nor is property (QT).

Keywords

generalised Baumslag–Solitar group, quasiisometry

Mathematical Subject Classification

Primary: 20F65

Secondary: 20F67

References

Publication

Received: 30 May 2023

Revised: 5 January 2024

Accepted: 28 March 2024

Published: 11 August 2025

Authors

Jack O Button
Selwyn College University of Cambridge Cambridge United Kingdom

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Volume 25, issue 4 (2025)