Rational embeddings of hyperbolic groups

2017/11/22 by Belk, James, Bleak, Collin, Matucci, Francesco · 1 citation
#20F10 #20F65 (Primary) 20F67 #68Q70 (Secondary) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1711.08369

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.

Cited by

• Horofunctions of infinite Sierpinski polygon graphs

Related

• Rationality of the Gromov Boundary of Hyperbolic Groups
• Hyperbolic groups with homeomorphic Gromov boundaries
• On the asynchronous rational group
• Gromov boundaries as Markov compacta
• Trees of Graphs as Boundaries of Hyperbolic Groups