Conjugator length in Thompson’s groups

Belk, J. and Matucci, F. (2023) Conjugator length in Thompson’s groups. Bulletin of the London Mathematical Society, 55(2), pp. 793-810. (doi: 10.1112/blms.12757)

Abstract

We prove Thompson's group F has quadratic conjugator length function. That is, for any two conjugate elements of F of length n or less, there exists an element of F of length O(n2) that conjugates one to the other. Moreover, there exist conjugate pairs of elements of F of length at most n such that the shortest conjugator between them has length Ω(n2). This latter statement holds for T and V as well.

• Item Type: Articles
• Additional Information: The first author has been partially supported by EPSRC grant EP/R032866/1 as well as the National Science Foundation under Grant No. DMS-1854367 during the creation of this paper. The second author is a member of the Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni (GNSAGA) of the Istituto Nazionale di Alta Matematica (INdAM) and gratefully acknowledges the support of the Fundação para a Ciência e a Tecnologia (CEMAT-Ciências FCT projects UIDB/04621/2020 and UIDP/04621/2020) and of the Università degli Studi di Milano–Bicocca (FA project ATE-2017-0035 “Strutture Algebriche”).
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Belk, Dr Jim
• Authors: Belk, J., and Matucci, F.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Bulletin of the London Mathematical Society
• Publisher: Wiley
• ISSN: 0024-6093
• ISSN (Online): 1469-2120
• Published Online: 10 December 2022
• Copyright Holders: Copyright © 2022 The Authors
• First Published: First published in Bulletin of the London Mathematical Society 55(2):793-810
• Publisher Policy: Reproduced under a Creative Commons License

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