Related papers: An embedding theorem for subshifts over amenable g…

We extend F{\o}lner's amenability criterion to the realm of general topological groups. Building on this, we show that a topological group $G$ is amenable if and only if its left translation action can be approximated in a uniform manner by…

Let $R$ be a ring, let $G$ be an amenable group and let $R\ast G$ be a crossed product. The goal of this paper is to construct, starting with a suitable additive function $L$ on the category of left modules over $R$, an additive function on…

In this work, we prove that every SFT, sofic shift, and strongly irreducible shift on locally finite groups has strong dynamical properties. These properties include that every sofic shift is an SFT, every SFT is strongly irreducible, every…

We prove that every dynamical system $X$ with free action of a countable amenable group $G$ by homeomorphisms has a zero-dimensional extension $Y$ which is faithful and principal, i.e. every $G$-invariant measure $\mu$ on $X$ has exactly…

Let $G$ be the group $\mathbb{Z}^d$ or the monoid $\mathbb{N}^d$ where $d$ is a positive integer. Let $X$ be a subshift over $G$, i.e., a closed and shift-invariant subset of $A^G$ where $A$ is a finite alphabet. We prove that the…

We suggest a modified and briefer version for the proof of Higman's embedding theorem stating that a finitely generated group can be embedded in a finitely presented group if and only if it is recursively presented. In particular, we…

Given any strong orbit equivalence class of minimal Cantor systems and any cardinal number that is finite, countable, or the continuum, we show that there exists a minimal subshift within the given class whose number of asymptotic…

We prove the Moore and the Myhill property for strongly irreducible subshifts over right amenable and finitely right generated left homogeneous spaces with finite stabilisers. Both properties together mean that the global transition…

We study projectivity in the category of $G$-flows and affine $G$-flows for Polish groups $G$. We also introduce the notion of \emph{proximally irreducible} extensions between affine $G$-flows. Using this we provide a characterization of…

We show that if $G$ is a countable amenable group, then every stationary non-Gaussian symmetric $\alpha$-stable (S$\alpha$S) process indexed by $G$ is ergodic if and only if it is weakly-mixing, and it is ergodic if and only if its Rosinski…

We demonstrate under appropriate finiteness conditions that a coarse embedding induces an inequality of homological Dehn functions. Applications of the main results include a characterization of what finitely presentable groups may admit a…

In this paper, we study the quasisymmetric embeddability of weak tangents of metric spaces. We first show that quasisymmetric embeddability is hereditary, i.e., if $X$ can be quasisymmetrically embedded into $Y$, then every weak tangent of…

An important question in dynamical systems is the classification problem, i.e., the ability to distinguish between two isomorphic systems. In this work, we study the topological factors between a family of multidimensional substitutive…

We construct an embedding G of the category of graphs into the category of abelian groups such that for graphs X and Y we have Hom(GX,GY)=Z[Hom(X,Y)], the free abelian group whose basis is the set Hom(X,Y). The isomorphism is functorial in…

In this paper we show that for every congruent monotileable amenable group $G$ and for every metrizable Choquet simplex $K$, there exists a minimal $G$-subshift, which is free on a full measure set, whose set of invariant probability…

The embedding theorem of Roelcke and Dierolf for the completions of four standard uniform structures on topological groups and their quotients holds more generally for spaces of uniform measures. The natural mappings between the four spaces…

Let $(X, \sigma)$ be a transitive sofic shift and let $\rm{Aut}(X)$ denote its automorphism group. We generalize a result of Frisch, Schlank, and Tamuz to show that any normal amenable subgroup of $\rm{Aut}(X)$ must be contained in the…

We show that if $(X,T)$ is an extension of an aperiodic subshift (a subsystem of $({1,2,...,l}^{\mathbb{Z}},\mathrm{shift})$ for some $l\in\mathbb{N}$) and has mean dimension $mdim(X,T)<\frac{D}{2}$ $(D\in \mathbb{N}$), then it embeds…

In this paper we prove two theorems. The first one is a structure result that describes the extrinsic geometry of an embedded surface with constant mean curvature (possibly zero) in a homogeneously regular Riemannian three-manifold, in any…

It is well known that a dense subgroup $G$ of the complex unitary group $U(d)$ cannot be amenable as a discrete group when $d>1$. When $d$ is large enough we give quantitative versions of this phenomenon in connection with certain estimates…