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Are free groups of different ranks bi-invariantly quasi-isometric?

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  26 February 2025

Jarek Kędra Open the ORCID record for Jarek Kędra [Opens in a new window]  and
Assaf Libman
Jarek Kędra*
Affiliation:
University of Aberdeen, Aberdeen, United Kingdom University of Szczecin, Szczecin, Poland
Assaf Libman
Affiliation:
University of Aberdeen, Aberdeen, United Kingdom
*
Corresponding author: Jarek Kędra; Email: kedra@abdn.ac.uk
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Abstract

We prove that a homomorphism between free groups of finite rank equipped with the bi-invariant word metrics associated with finite generating sets is a quasi-isometry if and only if it is an isomorphism.

Keywords

Free groupbi-invariant metricword metricquasi-isometry

MSC classification

Primary: 20F65: Geometric group theory
Type
Research Article
Information
Glasgow Mathematical Journal , First View , pp. 1 - 9
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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