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arXiv · 1711.08369

Rational embeddings of hyperbolic groups

James Belk·Collin Bleak·Francesco Matucci
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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 $G$, 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 $G$.

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James Belk, Collin Bleak, Francesco Matucci. 2018-10-29. Rational embeddings of hyperbolic groups. https://arxiv.org/abs/1711.08369

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