Rational embeddings of hyperbolic groups

Belk, J., Bleak, C. and Matucci, F. (2021) Rational embeddings of hyperbolic groups. Journal of Combinatorial Algebra, 5(2), pp. 123-183. (doi: 10.4171/JCA/52)

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We prove that all Gromov hyperbolic groups embed into the asynchronous rational group defined by Grigorchuk, Nekrashevych and Sushchanski˘ı. The proof involves assigning a system of binary addresses to points in the Gromov boundary of a hyperbolic group G, and proving that elements of G act on these addresses by asynchronous transducers. These addresses derive from a certain self-similar tree of subsets of G, whose boundary is naturally homeomorphic to the horofunction boundary of G.

Item Type:Articles
Additional Information:The first and second authors have been partially supported by EPSRC grant EP/R032866/1 during the creation of this paper.
Glasgow Author(s) Enlighten ID:Belk, Dr Jim
Authors: Belk, J., Bleak, C., and Matucci, F.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Combinatorial Algebra
Publisher:EMS Press
ISSN (Online):2415-6310
Published Online:15 June 2021
Copyright Holders:Copyright © 2021 European Mathematical Society
First Published:First published in Journal of Combinatorial Algebra 5(2): 123-183
Publisher Policy:Reproduced under a Creative Commons License
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