Related papers: Bratteli diagrams, translation flows and their $C^…

Given a Bratteli diagram D we consider the compact topological space formed by all infinite paths on D. Two such path are said to be tail-equivalent when they "have the same tail", i.e. when they eventually coincide. This equivalence…

In this paper, we introduce a C*-algebra associated to any substitution (via its Bratteli diagram model). We show that this C*-algebra contains the partial crossed product C*-algebra of the corresponding Bratteli-Vershik system and show…

We describe a class of rank-2 graphs whose C^*-algebras are AT algebras. For a subclass which we call rank-2 Bratteli diagrams, we compute the K-theory of the C*-algebra. We identify rank-2 Bratteli diagrams whose C*-algebras are simple and…

We study C*-algebras O_{\lambda} which arise in dynamics of the interval exchange transformations and measured foliations on compact surfaces. Using Koebe-Morse coding of geodesic lines, we establish a bijection between Bratteli diagrams of…

Given a system of coverings of k-graphs, we show that the cohomology of the resulting (k+1)-graph is isomorphic to that of any one of the k-graphs in the system. We then consider Bratteli diagrams of 2-graphs whose twisted C*-algebras are…

We construct an explicit family of finite-area, infinite-genus translation surfaces whose vertical translation flow is strongly mixing. This provides a positive answer to a question posed by Lindsey and Trevi\~no~\cite{LT}

We introduce a new class of partial actions of free groups on totally disconnected compact Hausdorff spaces, which we call convex subshifts. These serve as an abstract framework for the partial actions associated with finite separated…

We study the notion of isomorphism for generalized Bratteli diagrams and investigate properties preserved under isomorphism. We show that every generalized Bratteli diagram is isomorphic to an irreducible generalized Bratteli diagram. We…

In this second paper, we study the case of substitution tilings of R^d. The substitution on tiles induces substitutions on the faces of the tiles of all dimensions j=0, ..., d-1. We reconstruct the tiling's equivalence relation in a purely…

We associate a Bratteli-type diagram to AH-algebras arising from generalized diagonal connecting maps. We use this diagram to give an explicit description of the connected components of the spectrum of an associated canonical…

We study the symmetries and geodesics of an infinite translation surface which arises as a limit of translation surfaces built from regular polygons, studied by Veech. We find the affine symmetry group of this infinite translation surface,…

We study homeomorphisms of a Cantor set with $k$ ($k < +\infty$) minimal invariant closed (but not open) subsets; we also study crossed product C*-algebras associated to these Cantor systems and their certain orbit-cut sub-C*-algebras. In…

A $\lambda$-graph system $\frak L$ is a labeled Bratteli diagram with shift operation. It is a generalized notion of finite labeled graph and presents a subshifts. We will study continuous orbit equivalence of one-sided subshifts and…

The goal of this note is to study the action of the backward Rauzy-Veech algorithm on the translation surfaces with horizontal saddle connections. In particular, we prove that the orbit of a translation surface via the aforementioned…

Let T be an aperiodic and repetitive tiling of R^d with finite local complexity. Let O be its tiling space with canonical transversal X. The tiling equivalence relation R_X is the set of pairs of tilings in X which are translates of each…

This paper is a survey on general (simple and non-simple) Bratteli diagrams which focuses on the following topics: finite and infinite tail invariant measures on the path space $X_B$ of a Bratteli diagram $B$, existence of continuous…

We continue our study of orderings on Bratteli diagrams started in previous work, joint with Jan Kwiatkowski, where Bratteli diagrams of finite rank were considered. We extend the notions of languages, permutations (called correspondences…

A Bratteli diagram is a type of graph in which the vertices are split into finite subsets occupying an infinite sequence of levels, starting with a bottom level and moving to successively higher levels along edges connecting consecutive…

We study infinite translation surfaces which are Z-covers of compact translation surfaces. We obtain conditions ensuring that such surfaces have Veech groups which are Fuchsian of the first kind and give a necessary and sufficient condition…

We define a canonical relative commutant planar algebra from a strongly Markov inclusion of finite von Neumann algebras. In the case of a connected unital inclusion of finite dimensional C*-algebras with the Markov trace, we show this…