On Lipschitz functions on groups equipped with conjugation-invariant norms

Jarek Kędra

doi:10.4064/cm9173-8-2023

On Lipschitz functions on groups equipped with conjugation-invariant norms

Jarek Kędra^*

^*Corresponding author for this work

Mathematical Science

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	89-99
Number of pages	11
Journal	Colloquium Mathematicum
Volume	174
Issue number	1
DOIs	https://doi.org/10.4064/cm9173-8-2023
Publication status	Published - 9 Oct 2023

Bibliographical note

Funding Information:
This work was funded by Leverhulme Trust Research Project Grant RPG-2017-159. The author was partially supported by the Polish NCN grant 2017/27/B/ST1/01467.

Keywords

bi-invariant metric
Lipschitz function
quasimorphism

Access to Document

10.4064/cm9173-8-2023Licence: Unspecified

Cite this

@article{adb4897e1a9b42f4bad3c928c3416a87,

title = "On Lipschitz functions on groups equipped with conjugation-invariant norms",

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.",

keywords = "bi-invariant metric, Lipschitz function, quasimorphism",

author = "Jarek K{\c e}dra",

note = "Funding Information: This work was funded by Leverhulme Trust Research Project Grant RPG-2017-159. The author was partially supported by the Polish NCN grant 2017/27/B/ST1/01467. ",

year = "2023",

month = oct,

day = "9",

doi = "10.4064/cm9173-8-2023",

language = "English",

volume = "174",

pages = "89--99",

journal = "Colloquium Mathematicum",

issn = "0010-1354",

publisher = "Institute of Mathematics, Polish Academy of Sciences",

number = "1",

}

TY - JOUR

T1 - On Lipschitz functions on groups equipped with conjugation-invariant norms

AU - Kędra, Jarek

N1 - Funding Information: This work was funded by Leverhulme Trust Research Project Grant RPG-2017-159. The author was partially supported by the Polish NCN grant 2017/27/B/ST1/01467.

PY - 2023/10/9

Y1 - 2023/10/9

N2 - 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.

AB - 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.

KW - bi-invariant metric

KW - Lipschitz function

KW - quasimorphism

UR - http://www.scopus.com/inward/record.url?scp=85176411105&partnerID=8YFLogxK

U2 - 10.4064/cm9173-8-2023

DO - 10.4064/cm9173-8-2023

M3 - Article

AN - SCOPUS:85176411105

SN - 0010-1354

VL - 174

SP - 89

EP - 99

JO - Colloquium Mathematicum

JF - Colloquium Mathematicum

IS - 1

ER -

On Lipschitz functions on groups equipped with conjugation-invariant norms

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this