Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups

Fuente: arXiv
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Autori principali: Abbott, Carolyn, Hagen, Mark, Petyt, Harry, Zalloum, Abdul
Natura: Preprint
Pubblicazione: 2023
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author Abbott, Carolyn
Hagen, Mark
Petyt, Harry
Zalloum, Abdul
author_facet Abbott, Carolyn
Hagen, Mark
Petyt, Harry
Zalloum, Abdul
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2305_09742
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups
Abbott, Carolyn
Hagen, Mark
Petyt, Harry
Zalloum, Abdul
Geometric Topology
Group Theory
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.
title Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups
topic Geometric Topology
Group Theory
url https://arxiv.org/abs/2305.09742