A4 Refereed article in a conference publication
SFT covers for actions of the first Grigorchuk group
Authors: Grigorchuk, Rostislav; Salo, Ville
Editors: Bezushchak, O.; Drozd, Yu.; Etingof, P.; Futorny, V.; Grigorchuk, R.; Zelmanov, E.
Conference name: Ukraine Algebraic Conference
Publisher: American Mathematical Society
Publication year: 2025
Journal: Contemporary Mathematics
Book title : Modern Algebra Volume 2: Groups and Algebras
Volume: 830
First page : 127
Last page: 158
ISBN: 978-1-4704-7619-9
ISSN: 0271-4132
eISSN: 1098-3627
DOI: https://doi.org/10.1090/conm/830/16562
Publication's open availability at the time of reporting: No Open Access
Publication channel's open availability : Partially Open Access publication channel
Web address : https://doi.org/10.1090/conm/830/16562
Preprint address: https://arxiv.org/abs/2403.06480
We study symbolic dynamical representations of actions of the first Grigorchuk group G, namely its action on the boundary of the infinite rooted binary tree, its representation in the topological full group of a minimal substitutive Z-shift, and its representation as a minimal system of Schreier graphs. We show that the first system admits an SFT cover, and the latter two systems are conjugate to sofic subshifts on G, but are not of finite type.
Funding information in the publication:
The first author is supported by the Humboldt Foundation, and expresses his gratitude to the University of Bielefeld. Also, he is supported by the Travel Support for Mathematicians grant MP-TSM-00002045 from the Simons Foundation.
