相关论文: Topology of the Random Fibonacci Tiling Space

In this paper we consider uniformly random lozenge tilings of arbitrary domains approximating (after suitable normalization) a closed, simply-connected subset of $\mathbb{R}^2$ with piecewise smooth, simple boundary. We show that the local…

Usually, for extension of local maps, one uses multiplication by so called bump functions. However, majority of infinite-dimensional linear topological spaces do not have smooth bump functions. Therefore, in \cite{BR} we suggested a new…

We show that the cohomology ring of a finite-dimensional complex pointed Hopf algebra with an abelian group of group-like elements is finitely generated. Our strategy has three major steps. We first reduce the problem to the finite…

Finite topological spaces are in bijective correspondence with preorders on finite sets. We undertake their study using combinatorial tools that have been developed to investigate general discrete structures. A particular emphasis will be…

Kirch topology on $\mathbb N$ goes back to 1969, and is remarkable for being Hausdorff, connected, and locally connected. In this sense, it is analogous to the usual topology on $\mathbb C,$ yet, to the author's knowledge, there have been…

A natural extension of the Hopf-cyclic cohomology, with coefficients, is introduced to encompass topological Hopf algebras. The topological theory allows to work with infinite dimensional Lie algebras. Furthermore, the category of…

A relatively simple substitution for the Robinson tilings is presented, which requires only 56 tiles up to translation. In this substitution, due to Joan M. Taylor, neighboring tiles are substituted by partially overlapping patches of…

In this paper we introduce and study three new cardinal topological invariants called the cs*, cs-, and sb-characters. The class of topological spaces with countable cs*-character is closed under many topological operations and contains all…

We prove that for any infinite countable amenable group $G$, any $\epsilon > 0$ and any finite subset $K\subset G$, there exists a tiling (partition of $G$ into finite "tiles" using only finitely many "shapes"), where all the tiles are $(K;…

A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…

We give an application of a topological dynamics version of multidimensional Brown's lemma to tiling theory: given a tiling of an Euclidean space and a finite geometric pattern of points $F$, one can find a patch such that, for each scale…

Aperiodic point sets (or tilings) which can be obtained by the method of cut and projection from higher dimensional periodic sets play an important role for the description of quasicrystals. Their topological invariants can be computed…

We characterise high-dimensional topology that arises from a random Cech complex constructed on the circle. Expected Euler characteristic curve is computed, where we observe limiting spikes. The spikes correspond to expected Betti numbers…

Given an n-dimensional substitution whose associated linear expansion is unimodular and hyperbolic, we use elements of the one-dimensional integer \v{C}ech cohomology of the associated tiling space to construct a finite-to-one…

Wheeler emphasized the study of Superspace - the space of 3-geometries on a spatial manifold of fixed topology. This is a configuration space for GR; knowledge of configuration spaces is useful as regards dynamics and QM.In this Article I…

We compute the sheaf cohomology of a groupoid built from a local homeomorphism of a locally compact space $X$. In particular, we identify the twists over this groupoid, and its Brauer group. Our calculations refine those made by Kumjian,…

We study the topology and dynamics of subshifts and tiling spaces associated to non-primitive substitutions in one dimension. We identify a property of a substitution, which we call tameness, in the presence of which most of the possible…

This article presents an algebraic topology perspective on the problem of finding a complete coverage probability of a one dimensional domain $X$ by a random covering, and develops techniques applicable to the problem beyond the one…

We consider two relatively natural topologizations of the set of all cellular automata on a fixed alphabet. The first turns out to be rather pathological, in that the countable space becomes neither first-countable nor sequential. Also,…

For bi-Lipschitz homeomorphisms of a compact manifold it is known that topological entropy is always finite. For compact manifolds of dimension two or greater, we show that in the closure of the space of bi-Lipschitz homeomorphisms, with…