Related papers: Meyer sets, topological eigenvalues, and Cantor fi…

Let $M$ be a model set meeting two simple conditions: (1) the internal space $H$ is a product of $R^n$ and a finite group, and (2) the window $W$ is a finite union of disjoint polyhedra. Then any point pattern with finite local complexity…

Model sets are always Meyer sets but the converse is generally not true. In this work we show that for a repetitive Meyer multiple sets of $\mathbb{R}^d$ with associated dynamical system $(\mathbb{X}, \mathbb{R}^d)$, the property of being a…

A linear deformation of a Meyer set $M$ in $\RR^d$ is the image of $M$ under a group homomorphism of the group $[M]$ generated by $M$ into $\RR^d$. We provide a necessary and sufficient condition for such a deformation to be a Meyer set. In…

Model sets are always Meyer sets, but not vice-versa. This article is about characterizing model sets (general and regular) amongst the Meyer sets in terms of two associated dynamical systems. These two dynamical systems describe two very…

Let $f$ be a chain mixing continuous onto mapping from the Cantor set onto itself.Let $g$ be an aperiodic homeomorphism on the Cantor set. We show that homeomorphisms that are topologically conjugate to g approximate $f$ in the topology of…

We prove that a primitive substitution Delone set, which is pure point diffractive, is a Meyer set. This answers a question of J. C. Lagarias. We also show that for primitive substitution Delone sets, being a Meyer set is equivalent to…

The aim of this note is to provide a conceptually simple demonstration of the fact that repetitive model sets are characterized as the repetitive Meyer sets with an almost automorphic associated dynamical system.

Let f be a chain mixing continuous onto mapping from the Cantor set onto itself. Let g be a homeomorphism on the Cantor set that is topologically conjugate to a subshift. Then, homeomorphisms that are topologically conjugate to g…

Topological structure of minimal sets is studied for a dynamical system $(E,F)$ given by a fibre-preserving, in general non-invertible, continuous selfmap $F$ of a graph bundle $E$. These systems include, as a very particular case,…

We study structural and topological properties of nested set complexes of matroids with arbitrary building sets, proving that these complexes are vertex decomposable and admit convex ear decompositions. These results unify and generalize…

In this paper, we analyze the complexity of topological conjugacy of pointed Cantor minimal systems from the point of view of descriptive set theory. We prove that the topological conjugacy relation on pointed Cantor minimal systems is…

A meromorphic connection on the tangent bundle of a Riemann surface induces a complex affine structure on the complement of the poles. Local models for Fuchsian singularities are already known. In this paper, we introduce a complete set of…

We consider substitution tilings and Delone sets without the assumption of finite local complexity (FLC). We first give a sufficient condition for tiling dynamical systems to be uniquely ergodic and a formula for the measure of cylinder…

We study the topology of toric maps. We show that if $f\colon X\to Y$ is a proper toric morphism, with $X$ simplicial, then the cohomology of every fiber of $f$ is pure and of Hodge-Tate type. When the map is a fibration, we give an…

We obtain some new results on the topology of unary definable sets in densely ordered Abelian groups of burden groups of burden 2. In the special case in which the structure has dp-rank 2, we show that the existence of an infinite definable…

We prove linearly repetitive Delone systems have finitely many Delone system factors up to conjugacy. This result is also applicable to linearly repetitive tiling systems.

We establish necessary and sufficient conditions for a dynamical system to be topologically conjugate to the Morse minimal set, the shift orbit closure of the Morse sequence, and conditions for topological conjugacy to the closely related…

Serre and Abelson have produced examples of non-homeomorphic conjugate varieties. We show that if the field of definition of a polarized projective variety coincides with its field of moduli then all of its conjugates have the same…

In this paper, we focus attention on extending the topological conjugacy of adding machine maps and minimal systems to iterated function systems. We provide necessary and sufficient conditions for an iterated function system to be…

If a characteristic class for two vector bundles over the same base space does not coincide, then the bundles are not isomorphic. We give under rather common assumptions a lower bound on the topological dimension of the set of all points in…