Rational embeddings of hyperbolic groups

Autor(es)

Belk, James ^[1] ; Bleak, Collin ^[1] ; Matucci, Francesco ^[2]

Afiliação do(s) autor(es)

^[1] Univ St Andrews, Sch Math & Stat, St Andrews KY16 9SS, Fife - Scotland

^[2] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, I-20125 Milan - Italy

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF COMBINATORIAL ALGEBRA; v. 5, n. 2, p. 123-183, 2021.
• Citações Web of Science: 0

Resumo

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. (AU)

• Processo FAPESP: 16/12196-5 - Algoritmos e classificação em grupos
• Beneficiário: Francesco Matucci
• Modalidade de apoio: Auxílio à Pesquisa - Jovens Pesquisadores