Related papers: Polyhedral products for shifted complexes and high…

We show that the loop homology algebras of polyhedral products of the form $(\underline{X},\underline{*})^{\mathcal{K}}$ can be written as a colimit over the flagification of $\mathcal{K}$, and obtain a similar result for the Poincar\'e…

The notion of a dual polyhedral product is introduced as a generalization of Hovey's definition of Lusternik-Schnirelmann cocategory. Properties established from homotopy decompositions that relate the based loops on a polyhedral product to…

In this paper we define an associative stringy product for the twisted orbifold K-theory of a compact, almost complex orbifold X. This product is defined on the twisted K-theory of the inertia orbifold of X, where the twisting gerbe is…

For certain classes of holomorphic correspondences which are matings between Kleinian groups and polynomials, we prove the existence of pinching deformations, analogous to Maskit's deformations of Kleinian groups which pinch loxodromic…

We present some results on n-dimensional compacta lying in n-dimensional products of compacta, in particular, in products of n 1-dimensional compacta. Most of our basic results are proven under the assumption that the compacta X admit…

Let $K$ be a finite simplicial complex, and $(X,A)$ be a pair of spaces. The purpose of this article is to study the fundamental group of the polyhedral product denoted $Z_K(X,A)$, which denotes the moment-angle complex of Buchstaber-Panov…

In this paper, we construct Adams-Hilton models for the polyhedral products of spheres $(\underline{S})^{\mathcal{K}}$ and Davis-Januszkiewicz spaces $\left(\mathbb{C} P^{\infty}\right)^{\mathcal{K}}$. We show that in these cases the…

In this paper we study the classifying spaces of graph products of simplicial groups and connected Hopf algebras over a field, and show that they can be uniformly treated under the framework of polyhedral products. It turns out that these…

Let $I=(\mathbb{Z}^3,26,6,B)$ be a 3D digital image, let $Q(I)$ be the associated cubical complex and let $\partial Q(I)$ be the subcomplex of $Q(I)$ whose maximal cells are the quadrangles of $Q(I)$ shared by a voxel of $B$ in the…

We construct the crossed product of a C(X)-algebra by an endomorphism, in such a way that it becomes induced by a Hilbert C(X)-bimodule. Furthermore we introduce the notion of C(X)-category, and discuss relationships with crossed products…

The purpose of this paper is to exhibit fine structure for polyhedral products Z(K;(X,A) and polyhedral smash products $\widehat{Z}(K;(X,A)$. (Moment-angle complexes are special cases for which (X,A) = (D^2,S^1)). There are three main…

In this paper we establish a connection between the loop space homology of the generalization of wedge defined by a simplicial complex K (so called polyhedral product) and the homology of certain diagonal arrangements associated with K. We…

We describe the Goodwillie calculus of polyhedral products in the case that the fat wedge filtration on the associated real moment-angle complex is trivial. We do this by analysing the behaviour on calculus of the Denham-Suciu fibre…

We relate polyhedral products of topological spaces to graph products of groups. The loop homology algebras of polyhedral products are identified with the universal enveloping algebras of the Lie algebras associated with central series of…

We generalise the fold map for the wedge sum and use this to give a loop space decomposition of topological spaces with a high degree of symmetry. This is applied to polyhedral products to give a loop space decomposition of polyhedral…

Representation stability in the sense of Church-Farb is concerned with stable properties of representations of sequences of algebraic structures, in particular of groups. We study this notion on objects arising in toric topology. With a…

Generalizing a theorem of Macdonald, we show a formula for the mixed Hodge structure on the cohomology of the symmetric products of bounded complexes of mixed Hodge modules by showing the existence of the canonical action of the symmetric…

Discrete exterior calculus offers a coordinate--free discretization of exterior calculus especially suited for computations on meshes over curved manifolds. The discretization of the wedge product, that would be compatible with discrete…

We introduce a tree structure for the iterates of symmetric bimodal maps and identify a subset which we prove to be isomorphic to the family of unimodal maps. This subset is used as a second factor for a $\ast $-product that we define in…

In this paper we study the topological structure of moment-angle complexes $\mathcal{Z_K}$. We consider two classes of simplicial complexes. The first class $B_{\Delta}$ consists of simplicial complexes $\mathcal{K}$ for which…