Ends of Schreier graphs and cut-points of limit spaces of self-similar groups

Ievgen Bondarenko*, Daniele D'Angeli, Tatiana Nagnibeda

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Every self-similar group acts on the space X-omega of infinite words over some alphabet X. We study the Schreier graphs Gamma(w) for w is an element of X-omega of the action of self-similar groups generated by bounded automata on the space X-omega. Using sofic subshifts we determine the number of ends for every Schreier graph. w. Almost all Schreier graphs Gamma(w) with respect to the uniform measure on X-omega have one or two ends, and we characterize bounded automata whose Schreier graphs have two ends almost surely. The connection with (local) cut-points of limit spaces of self-similar groups is established.
Original languageEnglish
Article number4
Pages (from-to)369-424
JournalJournal of Fractal Geometry
Volume4
Issue number4
DOIs
Publication statusPublished - 2017

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