Rational embeddings of hyperbolic groups
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We prove that all Gromov hyperbolic groups embed into the asynchronous rational group defined by Grigorchuk, Nekrashevych and Sushchanski.i. 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.
Belk , J , Bleak , C & Matucci , F 2021 , ' Rational embeddings of hyperbolic groups ' , Journal of Combinatorial Algebra , vol. 5 , no. 2 , pp. 123-183 . https://doi.org/10.4171/JCA/52
Journal of Combinatorial Algebra
Copyright © 2021 European Mathematical Society Published by EMS Press. This work is licensed under a CC BY 4.0 license.
DescriptionFunding: The first and second authors have been partially supported by EPSRC grant EP/R032866/1 during the creation of this paper. The third author is a member of the Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni (GN-SAGA) of the Istituto Nazionale di Alta Matematica (INdAM) and gratefully acknowledges the support of the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP Jovens Pesquisadores em Centros Emergentes grant 2016/12196-5), of the Conselho Nacional de Desenvolvimento Cientfíco e Tecnológico (CNPq Bolsa de Produtividade emPesquisa PQ-2 grant 306614/2016-2) and of the Fundação para a Ciência e a Tecnologia (CEMAT-Ciências FCT projects UIDB/04621/2020 and UIDP/04621/2020).
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