相关论文: On actions of abelian Cantor groups

By a Cantor group we mean a topological group homeomorphic to the Cantor set. We show that a compact metric space of rational cohomological dimension $n$ can be obtained as the orbit space of a Cantor group action on a metric compact space…

We carry out the Cantor-Bendixson analysis of the space of all subgroups of any countable abelian group and we deduce a complete classification of such spaces up to homeomorphism.

We show that every minimal action of any finitely generated abelian group on the Cantor set is (topologically) orbit equivalent to an AF relation. As a consequence, this extends the classification up to orbit equivalence of minimal…

In this paper we investigate the action of Polish groups (not necessary abelian) on an uncountable Polish spaces. We consider two main situations. First, when the orbits given by group action are small and the second when the family of…

The purpose of this note is twofold. In the first part we observe that two finitely generated non-amenable groups are quasi-isometric if and only if they admit topologically orbit equivalent Cantor minimal actions. In particular, free…

A natural topology on the set of left orderings on free abelian groups and free groups $F_n$, $n>1$ has studied in [1]. It has been proven already that in the abelian case the resulted topological space is a Cantor set. There was a…

A natural topology on the space of left orderings of an arbitrary semi-group is introduced. It is proved that this space is compact and that for free abelian groups it is homeomorphic to the Cantor set. An application of this result is a…

This paper gives an algebraic characterization of expansive actions of countable abelian groups on compact abelian groups. This naturally extends the classification of expansive algebraic $\mathbb{Z}^d$-actions given by Schmidt using…

Cohomology for actions of free abelian groups on the Cantor set has (when endowed with an order structure) provided a complete invariance for orbit equivalence. In this paper, we study a particular class of actions of such groups called…

We describe the envelope C*-algebra associated to a partial action of a countable discrete group on a locally compact space as a groupoid C*-algebra (more precisely as a C*-algebra from an equivalence relation) and we use our approach to…

Grigorchuk and Medynets recently announced that the topological full group of a minimal Cantor Z-action is amenable. They asked whether the statement holds for all minimal Cantor actions of general amenable groups as well. We answer in the…

We specify exactly which groups can act geometrically on CAT(0) spaces whose visual boundary is homeomorphic to either a circle or a suspension of a Cantor set.

We show that every topological grading of a C*-algebra by a discrete abelian group is implemented by an action of the compact dual group.

We introduce and study the notion of continuous orbit equivalence of actions of countable discrete groups on Cartan pairs in (twisted) groupoid context. We characterize orbit equivalence of actions in terms of the corresponding…

We give a classification and complete algebraic description of groups allowing only finitely many (left multiplication invariant) circular orders. In particular, they are all solvable groups with a specific semi-direct product…

We consider a finitely generated group acting minimally on a compact space by homeomorphsims, and assume that the Schreier graph of at least one orbit is quasi-isometric to a line. We show that the topological full group of such an action…

We show that the (topological) full group of a minimal pseudogroup over the Cantor set satisfies various rigidity phenomena of topological dynamical and combinatorial nature. Our main result applies to its possible homomorphisms into other…

We introduce a notion of entropy for automorphisms of discrete groups which admit amenable actions on a compact space. This entropy is dual to classical topological entropy in the sense that if G is discrete and abelian then our notion of…

In this paper, we give a characterization of the action of any abelian subgroup G of GL(n, C) on C^n. We prove that any orbit of G is regular with order m<=2n. Moreover, we give a method to determine this order. In the other hand, we…

We calssify actions of discrete abelian groups on some inclusions of von Neumann algebras, up to cocycle conjugacy. As an application, we classify actions of compact abelian groups on the inclusions of AFD factors of type II_1 with index…