Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups

Carolyn Abbott; Mark Hagen; Harry Petyt; Abdul Zalloum

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arXiv · 2305.09742

Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups

Carolyn Abbott·Mark Hagen·Harry Petyt·Abdul Zalloum

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Abstract

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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BibTeX RIS

Carolyn Abbott, Mark Hagen, Harry Petyt, Abdul Zalloum. 2023-05-16. Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups. https://arxiv.org/abs/2305.09742

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