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Rational embeddings of hyperbolic groups
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dc.contributor.author | Belk, James | |
dc.contributor.author | Bleak, Collin | |
dc.contributor.author | Matucci, Francesco | |
dc.date.accessioned | 2021-07-15T12:30:04Z | |
dc.date.available | 2021-07-15T12:30:04Z | |
dc.date.issued | 2021-06-15 | |
dc.identifier | 252044252 | |
dc.identifier | 5194a3b1-62e8-4c85-8376-539a899140f8 | |
dc.identifier | 000661936500002 | |
dc.identifier | 85110005528 | |
dc.identifier.citation | 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 | en |
dc.identifier.issn | 2415-6302 | |
dc.identifier.other | ORCID: /0000-0001-5790-1940/work/96489455 | |
dc.identifier.uri | https://hdl.handle.net/10023/23580 | |
dc.description | Funding: 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 (GNSAGA) 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.abstract | We prove that all Gromov hyperbolic groups embed into the asynchronous rational group defined by Grigorchuk, Nekrashevych and Sushchanskii. 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.extent | 61 | |
dc.format.extent | 2121628 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of Combinatorial Algebra | en |
dc.subject | Hyperbolic groups | en |
dc.subject | Rational group | en |
dc.subject | Gromov boundary | en |
dc.subject | Horofunction boundary | en |
dc.subject | Transducers | en |
dc.subject | QA Mathematics | en |
dc.subject | Algebra and Number Theory | en |
dc.subject | Discrete Mathematics and Combinatorics | en |
dc.subject | T-NDAS | en |
dc.subject | MCC | en |
dc.subject.lcc | QA | en |
dc.title | Rational embeddings of hyperbolic groups | en |
dc.type | Journal article | en |
dc.contributor.sponsor | EPSRC | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. School of Mathematics and Statistics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | 10.4171/JCA/52 | |
dc.description.status | Peer reviewed | en |
dc.identifier.grantnumber | EP/R032866/1 | en |
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