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Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups

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arxiv 2305.09742 v2 pith:LCCXLNXN submitted 2023-05-16 math.GT math.GR

Carolyn Abbott , Mark Hagen , Harry Petyt , Abdul Zalloum This is my paper · ORCID
classification math.GTmath.GR
keywords groupshyperbolichierarchicallyspacesuniformlyactingactionsapplications
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We show that infinite cyclic subgroups of groups acting uniformly properly on injective metric spaces are uniformly undistorted. In the special case of hierarchically hyperbolic groups, we use this to study translation lengths for actions on the associated hyperbolic spaces. We then use quasimorphisms to produce examples where these latter results are sharp.

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  1. Bounded cohomology, quotient extensions, and hierarchical hyperbolicity

    math.GR 2025-05 conditional novelty 6.0 of 10

    A central extension of a hierarchically hyperbolic group is hierarchically hyperbolic if and only if its Euler class is bounded.

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