On Lipschitz functions on groups equipped with conjugation-invariant norms
Group Theory
2023-08-04 v3 Metric Geometry
Abstract
We observe that a function on a group equipped with a bi-invariant word metric is Lipschitz if and only if it is a partial quasimorphism bounded on the generating set. We also show that an undistorted element is always detected by an antisymmetric homogeneous partial quasimorphisms. We provide a general homogenisation procedure for Lipschitz functions and relate partial quasimorphisms on a group to ones on its asymptotic cones.
Cite
@article{arxiv.2204.09373,
title = {On Lipschitz functions on groups equipped with conjugation-invariant norms},
author = {Jarek Kędra},
journal= {arXiv preprint arXiv:2204.09373},
year = {2023}
}
Comments
11 pages; minor corrections