Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups
Geometric Topology
2025-05-27 v2 Group Theory
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.
Keywords
Cite
@article{arxiv.2305.09742,
title = {Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups},
author = {Carolyn Abbott and Mark Hagen and Harry Petyt and Abdul Zalloum},
journal= {arXiv preprint arXiv:2305.09742},
year = {2025}
}
Comments
32 pages. v2: Accepted version