Notes on the Schreier graphs of the Grigorchuk group
Yaroslav Vorobets
TL;DR
This paper studies the structure and dynamics of Schreier graphs associated with the Grigorchuk group, focusing on an invariant set related to the boundary of the binary rooted tree and analyzing the group's action on this set.
Contribution
It characterizes an invariant subset of Schreier graphs and describes the dynamics of the Grigorchuk group's action on this set, advancing understanding of its geometric and dynamical properties.
Findings
Identification of an invariant set of Schreier graphs
Description of the group's action dynamics on this set
Insights into the boundary behavior of the Grigorchuk group
Abstract
The paper is concerned with the space of the marked Schreier graphs of the Grigorchuk group and the action of the group on this space. In particular, we describe an invariant set of the Schreier graphs corresponding to the action on the boundary of the binary rooted tree and dynamics of the group action restricted to this invariant set.
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Taxonomy
Topicsadvanced mathematical theories · Topological and Geometric Data Analysis · Advanced Algebra and Geometry