Related papers: Wild Cantor actions

A generalization of the double commutator lemma for normal subgroups is shown for invariant random subgroups of a countable group acting faithfully on a Hausdorff space. As an application, we classify ergodic invariant random subgroups of…

We extend Forester's rigidity theorem so as to give a complete characterization of rigid group actions on trees (an action is rigid if it is the only reduced action in its deformation space, in particular it is invariant under automorphisms…

In the first part of this work we have established an efficient method to obtain a topological classification of locally discrete, finitely generated, virtually free subgroups of real-analytic circle diffeomorphisms. In this second part we…

We introduce the property of having good subgroups for actions of countable discrete groups on compact metrizable spaces, and show that it implies comparison when the acting group is amenable. As a consequence, free actions on…

We consider the actions of (semi)groups on a locally compact group by automorphisms. We show the equivalence of distality and pointwise distality for the actions of a certain class of groups. We also show that a compactly generated locally…

Automorphism groups of locally finite trees provide a large class of examples of simple totally disconnected locally compact groups. It is desirable to understand the connections between the global and local structure of such a group.…

We extend the proof of automatic continuity for homeomorphism groups of manifolds to non-compact manifolds and manifolds with marked points and their mapping class groups. Specifically, we show that, for any manifold $M$ homeomorphic to the…

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…

Let $T$ be a tree and $e$ an edge in $T$. If $C$ is a component of $T\setminus e$ and both $C$ and its complement are infinite we say that $C$ is a half-tree. The main result of this paper is that if $G$ is a closed subgroup of the…

We show that every group acting freely and vertex-transitively by isometries on a product of two regular trees of finite valence is boundary rigid. That means that every CAT(0) space that admits a geometric action of any such group has the…

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…

The paper is concerned with maximal subgroups of the ample (better known as topological full) groups of homeomorphisms of totally disconnected compact metrizable topological spaces. We describe all maximal subgroups that are stabilizers of…

It is shown that the restriction of the action of any group with finite orbit on the minimal sets of dendrites is equicontinuous. Consequently, we obtain that the action of any amenable group and Thompson group on dendrite restricted on…

In the present note we focus on dynamics on the Gehman dendrite $\mathcal{G}$. It is well-known that the set of its endpoints is homeomorphic to a standard Cantor ternary set. For any given surjective Cantor system $\mathcal{C}$ we provide…

Let $T$ be a locally finite tree all of whose vertices have valency at least $6$. We classify, up to isomorphism, the closed subgroups of $\mathrm{Aut}(T)$ acting $2$-transitively on the set of ends of $T$ and whose local action at each…

Each topological group $G$ admits a unique universal minimal dynamical system $(M(G),G)$. When $G$ is a non-compact locally compact group the phase space $M(G)$ of this universal system is non-metrizable. There are however topological…

We prove that a crossed product algebra arising from a minimal dynamical system on the product of the Cantor set and the circle has real rank zero if and only if that system is rigid. In the case that cocycles take values in the rotation…

Given any pair of countable groups $G$ and $H$ with $G$ infinite, we construct a minimal, free, Cantor $G$-flow $X$ so that $H$ embeds into the group of automorphisms of $X$.

We study actions of discrete groups on contractible topological spaces in which either (1) all stabilizers lie in the family of subgroups of prime power order or (2) all stabilizers lie in the family of finite subgroups. We compare the…

We construct different types of quasiperiodically forced circle homeomorphisms with transitive but non-minimal dynamics. Concerning the recent Poincar\'e-like classification for this class of maps of Jaeger-Stark, we demonstrate that…