Generalised Baumslag-Solitar groups and Hierarchically Hyperbolic Groups

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Generalised Baumslag-Solitar groups and Hierarchically Hyperbolic Groups

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arxiv 2208.12688 v2 pith:NOZPV72D submitted 2022-08-26 math.GR

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keywords hyperbolicgroupshierarchicallyarbitrarygeneralisedgroupinvariantabelian

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

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Central extensions and proper actions on products of hyperbolic spaces
math.GR 2025-06 accept novelty 8.0 of 10

A central extension preserves property (PH) or (QT) exactly when its Euler class is bounded.

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