Related papers: Triangulations of simplicial complexes and theta p…

Let X be a projective scheme carrying a circle action S with isolated fixed points. We associate a simplicial complex Delta(X,S) of "closure chains" using a refinement of its Morse/Bialynicki-Birula decomposition. If this decomposition is a…

Let Y be a random d-dimensional subcomplex of the (n-1)-dimensional simplex S obtained by starting with the full (d-1)-dimensional skeleton of S and then adding each d-simplex independently with probability p=c/n. We compute an explicit…

Given a manifold with corners $X$, we associates to it the corner structure simplicial complex $\Sigma_X$. Its reduced K-homology is isomorphic to the K-theory of the $C^*$-algebra $\mathcal{K}_b(X)$ of b-compact operators on $X$. Moreover,…

A simplicial complex is a set equipped with a down-closed family of distinguished finite subsets. This structure, usually viewed as codifying a triangulated space, is used here directly, to describe "spaces" whose geometric realisation can…

A trinomial algebra is a commutative finitely generated algebra given by a system of compatible relations each of which is a polynomial with three terms. Such algebras arise as the Cox rings of varieties admitting a complexity one torus…

The theory of bi-orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to…

We construct embeddings of simplicial complexes into a (surface of a) simplicial ball whose triangulation has bounded degrees and low volume. This construction can be used either to efficiently "simplify a complicated space" by realizing it…

In this article we prove some theorems related to the triplets of triangles, homological two by two. These theorems will be used later to build triplets of triangles two by two tri-homological.

We prove that the simplicial complex $\Delta _{\mathcal{C}_n,2}$ is pure and a weak pseudomanifold of dimension $2(n-1)$, where $\Delta _{\mathcal{C}_n,2}$ is the simplicial complex associated with $2$-triangulations on the half-cylinder…

We develop a framework for computing the homology of weighted simplicial complexes with coefficients in a discrete valuation ring. A weighted simplicial complex, $(X,v)$, introduced by Dawson [Cah. Topol. G\'{e}om. Diff\'{e}r. Cat\'{e}g. 31…

Simplicial versions of topological abelian gauge theories are constructed which reproduce the continuum expressions for the partition function and Wilson expectation value of linked loops, expressible in terms of R-torsion and linking…

The intersection matrix of a simplicial complex has entries equal to the rank of the intersection of its facets. In [1] the authors prove the intersection matrix is enough to determine a triangulation of a surface up to isomorphism. In this…

Counting Euclidean triangulations with vertices in a finite set $\C$ of the convex hull $\conv(\C)$ of $\C$ is difficult in general, both algorithmically and theoretically. The aim of this paper is to describe nearly convex polygons, a…

Let $\Delta$ be an one-dimensional simplicial complex on $\{1,2,\ldots,s\}$ and $S$ the polynomial ring $K[x_1,\ldots,x_s]$ over a field $K$. The explicit formula for $a_0(S/I_{\Delta}^n)$ is presented when $\mathrm{girth}(\Delta)\geq 4$.…

In 1971, McMullen and Walkup posed the following conjecture, which is called the generalized lower bound conjecture: If $P$ is a simplicial $d$-polytope then its $h$-vector $(h_0,h_1,...,h_d)$ satisfies $h_0 \leq h_1 \leq ... \leq…

In this paper we prove that every definable set has a definable triangulation which is locally Lipschitz and weakly bi-Lipschitz on the natural simplicial stratification of the simplicial complex. We also distinguish a class T of regularity…

In a seminal paper Richard Stanley derived Pieri rules for the Jack symmetric function basis. These rules were extended by Macdonald to his now famous symmetric function basis. The original form of these rules had a forbidding complexity…

Stanley's symmetrized chromatic polynomial is a generalization of the ordinary chromatic polynomial to a graph invariant with values in a ring of polynomials in infnitely many variables. The ordinary chromatic polynomial is a specialization…

We extend many theorems from the context of solid angle sums over rational polytopes to the context of solid angle sums over real polytopes. Moreover, we consider any real dilation parameter, as opposed to the traditional integer dilation…

In this paper we investigate the simplicial structure of a chain complex associated to the higher order Hochschild homology over the $3$-sphere. We also introduce the tertiary Hochschild homology corresponding to a quintuple…