# On Lipschitz functions on groups equipped with conjugation-invariant norms

Source: [On Lipschitz functions on groups equipped with conjugation-invariant norms](<https://www.sota2.com/research/paper/68fa5ab41e209131ce9c21d8>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T16:39:50.279Z

Authors: Jarek K\\k{e}dra

Published: 2022-04-20T10:28:03.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2204.09373>)

[PDF](<https://arxiv.org/pdf/2204.09373.pdf>)