Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups

Carolyn Abbott; Mark Hagen; Harry Petyt; Abdul Zalloum

Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups

Carolyn Abbott, Mark Hagen, Harry Petyt, Abdul Zalloum

School of Mathematics

Research output: Working paper › Preprint

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Abstract

We show that infinite cyclic subgroups of groups acting uniformly metrically 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. Then we use quasimorphisms to produce examples where these latter results are sharp.

Original language	English
Publication status	Submitted - 16 May 2023

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math.GT
math.GR

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This is the submitted manuscript (SM). It first appeared online via arXiv at https://doi.org/10.48550/arXiv.2305.09742. Please refer to any applicable terms of use of the publisher.
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AB - We show that infinite cyclic subgroups of groups acting uniformly metrically 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. Then we use quasimorphisms to produce examples where these latter results are sharp.

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Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups

Abstract

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