Rational embeddings of hyperbolic groups
James Belk
University of St Andrews, UKCollin Bleak
University of St Andrews, UKFrancesco Matucci
Universita Degli Studi Di Milano Bicocca, Italy
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Abstract
We prove that all Gromov hyperbolic groups embed into the asynchronous rational group defined by Grigorchuk, Nekrashevych and Sushchanskiĭ. The proof involves assigning a system of binary addresses to points in the Gromov boundary of a hyperbolic group , and proving that elements of act on these addresses by asynchronous transducers. These addresses derive from a certain self-similar tree of subsets of , whose boundary is naturally homeomorphic to the horofunction boundary of .
Cite this article
James Belk, Collin Bleak, Francesco Matucci, Rational embeddings of hyperbolic groups. J. Comb. Algebra 5 (2021), no. 2, pp. 123–183
DOI 10.4171/JCA/52