Combinatorics of the subshift associated to Grigorchuk's group

Abstract

We study combinatorial properties of the subshift induced by the substitution that describes Lysenok's presentation of Grigorchuk's group of intermediate growth by generators and relators. This subshift has recently appeared in two different contexts: on one hand, it allowed to embed Grigorchuk's group in a topological full group, and on the other hand, it was useful in the spectral theory of Laplacians on the associated Schreier graphs.

8 pages; part of the material discussed in the paper was originally contained in (earlier versions of) arXiv:1510.00545 and arXiv:1412.6822. In their published versions the latter two articles do not contain this material anymore