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arXiv · 2403.06480

SFT covers for actions of the first Grigorchuk group

Rostislav Grigorchuk·Ville Salo
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Abstract

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 $\mathbb{Z}$-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.

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Rostislav Grigorchuk, Ville Salo. 2024-03-11. SFT covers for actions of the first Grigorchuk group. https://arxiv.org/abs/2403.06480

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