ﻻ يوجد ملخص باللغة العربية
A nilpotent Cantor action is a minimal equicontinuous action $Phi colon Gamma times frak{X} to frak{X}$ on a Cantor set $frak{X}$, where $Gamma$ contains a finitely-generated nilpotent subgroup $Gamma_0 subset Gamma$ of finite index. In this note, we show that these actions are distinguished among general Cantor actions: any effective action of a finitely generated group on a Cantor space, which is continuously orbit equivalent to a nilpotent Cantor action, must itself be a nilpotent Cantor action. As an application of this result, we obtain new invariants of nilpotent Cantor actions under continuous orbit equivalence.
In this paper, we consider minimal equicontinuous actions of discrete countably generated groups on Cantor sets, obtained from the arboreal representations of absolute Galois groups of fields. In particular, we study the asymptotic discriminant of th
The discriminant group of a minimal equicontinuous action of a group $G$ on a Cantor set $X$ is the subgroup of the closure of the action in the group of homeomorphisms of $X$, consisting of homeomorphisms which fix a given point. The stabilizer and
In this paper, we study the actions of profinite groups on Cantor sets which arise from representations of Galois groups of certain fields of rational functions. Such representations are associated to polynomials, and they are called profinite iterat
We consider a minimal equicontinuous action of a finitely generated group $G$ on a Cantor set $X$ with invariant probability measure $mu$, and stabilizers of points for such an action. We give sufficient conditions under which there exists a subgroup
In this work, we investigate the dynamical and geometric properties of weak solenoids, as part of the development of a calculus of group chains associated to Cantor minimal actions. The study of the properties of group chains was initiated in the wor