Uniform undistortion from barycentres, and applications to hierarchically hyperbolic groups

2023/05/16 by Carolyn Abbott, M. Hagen, Abbott, Carolyn +5
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2305.09742

openalex publication_date 2023/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Finitely generated groups acting uniformly properly on hyperbolic space
• Properly discontinuous actions versus uniform embeddings
• A non-residually finite group acting uniformly properly on a hyperbolic space
• Generalised Baumslag-Solitar groups and Hierarchically Hyperbolic Groups
• Hierarchically hyperbolic groups and uniform exponential growth