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dc.contributor.authorBelk, James
dc.contributor.authorBleak, Collin
dc.contributor.authorMatucci, Francesco
dc.date.accessioned2021-07-15T12:30:04Z
dc.date.available2021-07-15T12:30:04Z
dc.date.issued2021-06-15
dc.identifier.citationBelk , 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/52en
dc.identifier.issn2415-6302
dc.identifier.otherPURE: 252044252
dc.identifier.otherPURE UUID: 5194a3b1-62e8-4c85-8376-539a899140f8
dc.identifier.otherWOS: 000661936500002
dc.identifier.otherORCID: /0000-0001-5790-1940/work/96489455
dc.identifier.otherScopus: 85110005528
dc.identifier.urihttp://hdl.handle.net/10023/23580
dc.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).en
dc.description.abstractWe 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.
dc.format.extent61
dc.language.isoeng
dc.relation.ispartofJournal of Combinatorial Algebraen
dc.rightsCopyright © 2021 European Mathematical Society Published by EMS Press. This work is licensed under a CC BY 4.0 license.en
dc.subjectHyperbolic groupsen
dc.subjectRational groupen
dc.subjectGromov boundaryen
dc.subjectHorofunction boundaryen
dc.subjectTransducersen
dc.subjectQA Mathematicsen
dc.subjectAlgebra and Number Theoryen
dc.subjectDiscrete Mathematics and Combinatoricsen
dc.subjectT-NDASen
dc.subject.lccQAen
dc.titleRational embeddings of hyperbolic groupsen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews.School of Mathematics and Statisticsen
dc.contributor.institutionUniversity of St Andrews.Centre for Interdisciplinary Research in Computational Algebraen
dc.identifier.doihttps://doi.org/10.4171/JCA/52
dc.description.statusPeer revieweden


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