We prove that all Gromov hyperbolic groups embed into the asynchronous rational group defined by Grigorchuk, Nekrashevych and Sushchanskiǐ. 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, 5(2), 123-183 [10.4171/JCA/52].
Citazione: | Belk, J., Bleak, C., & Matucci, F. (2021). Rational embeddings of hyperbolic groups. JOURNAL OF COMBINATORIAL ALGEBRA, 5(2), 123-183 [10.4171/JCA/52]. | |
Tipo: | Articolo in rivista - Articolo scientifico | |
Carattere della pubblicazione: | Scientifica | |
Presenza di un coautore afferente ad Istituzioni straniere: | Si | |
Titolo: | Rational embeddings of hyperbolic groups | |
Autori: | Belk, J; Bleak, C; Matucci, F | |
Autori: | ||
Data di pubblicazione: | 2021 | |
Lingua: | English | |
Rivista: | JOURNAL OF COMBINATORIAL ALGEBRA | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.4171/JCA/52 | |
Appare nelle tipologie: | 01 - Articolo su rivista |
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