Rational embeddings of hyperbolic groups
| Autor: | Collin Bleak, Francesco Matucci, James Belk |
|---|---|
| Přispěvatelé: | EPSRC, University of St Andrews. Pure Mathematics, University of St Andrews. School of Mathematics and Statistics, University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra, Belk, J, Bleak, C, Matucci, F |
| Rok vydání: | 2021 |
| Předmět: |
MCC
Algebra and Number Theory Transducers T-NDAS Rational group Group Theory (math.GR) MAT/02 - ALGEBRA Horofunction boundary Hyperbolic groups Gromov boundary FOS: Mathematics Mathematics::Metric Geometry Discrete Mathematics and Combinatorics QA Mathematics 20F65 (Primary) 20F67 20F10 68Q70 (Secondary) QA Mathematics - Group Theory Humanities Hyperbolic group Mathematics |
| Zdroj: | Journal of Combinatorial Algebra. 5:123-183 |
| ISSN: | 2415-6302 |
| Popis: | We prove that all Gromov hyperbolic groups embed into the asynchronous rational group defined by Grigorchuk, Nekrashevych and Sushchanski\u{i}. The proof involves assigning a system of binary addresses to points in the Gromov boundary of $G$, and proving that elements of $G$ act on these addresses by transducers. These addresses derive from a certain self-similar tree of subsets of $G$, whose boundary is naturally homeomorphic to the horofunction boundary of $G$. Comment: 73 pages, 17 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|