On Lipschitz functions on groups equipped with conjugation-invariant norms
Volume 174 / 2023
Colloquium Mathematicum 174 (2023), 89-99
MSC: Primary 20F65; Secondary 51F30.
DOI: 10.4064/cm9173-8-2023
Published online: 9 October 2023
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 a generating set. We also show that an undistorted element is always detected by an antisymmetric homogeneous partial quasimorphism. We provide a general homogenisation procedure for Lipschitz functions and relate partial quasimorphisms on a group to ones on its asymptotic cones.
