Related papers: Obstructions to shellability, partitionability, an…
The matching complex $M(G)$ of a graph $G$ is the set of all matchings in $G$. A Buchsbaum simplicial complex is a generalization of both a homology manifold and a Cohen--Macaulay complex. We give a complete characterization of the graphs…
We consider the canonical quantization of fermions on an odd dimensional manifold with boundary, with respect to a family of elliptic hermitean boundary conditions for the Dirac hamiltonian. We show that there is a topological obstruction…
The obstructions for an arbitrary fusion algebra to be a fusion algebra of some semisimple monoidal category are constructed. Those obstructions lie in groups which are closely related to the Hochschild cohomology of fusion algebras with…
Starting from an unpublished conjecture of Kalai and from a conjecture of Eisenbud, Green and Harris, we study several problems relating h-vectors of Cohen-Macaulay, flag simplicial complexes and face vectors of simplicial complexes.
We study bubbling for sequences of Yang-Mills connections on closed four-manifolds and we derive a compatibility of Pohozaev type between the weak limit connection and the bubble formed at a concentration point, involving the Weyl tensor of…
We define and study the notion of a minimal Cohen-Macaulay simplicial complex. We prove that any Cohen-Macaulay complex is shelled over a minimal one in our sense, and we give sufficient conditions for a complex to be minimal…
In this paper, we investigate a relation between finite graphs, simplicial flag complexes and right-angled Coxeter groups, and we provide a class of reconstructible finite graphs. We show that if $\Gamma$ is a finite graph which is the…
We consider the notion of a connection on a module over a commutative ring, and recall the obstruction calculus for such connections. The obstruction calculus is defined using Hochschild cohomology. However, in order to compute with Grobner…
Delaunay has shown that the Delaunay complex of a finite set of points $P$ of Euclidean space $\mathbb{R}^m$ triangulates the convex hull of $P$, provided that $P$ satisfies a mild genericity property. Voronoi diagrams and Delaunay…
Many structured systems admit locally consistent descriptions that nevertheless fail to globalize when constrained by an ambient reference or feasibility condition. Diagnosing such failures is naturally an evaluative problem: given a fixed…
In the present paper we describe topological obstructions to embedding of a (complex) matrix algebra bundle into a trivial one under some additional arithmetic condition on their dimensions. We explain a relation between this problem and…
Suppose $X$ is a smooth complex algebraic variety. A necessary condition for a complex topological vector bundle on $X$ (viewed as a complex manifold) to be algebraic is that all Chern classes must be algebraic cohomology classes, i.e., lie…
We calculate a certain homological obstruction introduced by De Concini, Procesi and Salvetti in their study of the Schwartz genus of the fibration from the space of ordered configuration of points in the plane to the space of the unordered…
Let $(A,\mathfrak{m})$ be a Cohen-Macaulay local ring with residue field $k$. If $M$ is a finitely generated $A$-module then set $\text{curv}(M) = \limsup_n\sqrt[n]{\beta_n^A(M)}$. We show that under mild hypotheses the existence of a…
We develop an obstruction theory for the extension of truncated minimal $A$-infinity bimodule structures over truncated minimal $A$-infinity algebras. Obstructions live in far-away pages of a (truncated) fringed spectral sequence of…
We study combinatorial and algebraic properties of $t$-clique-free complexes, a family of simplicial complexes associated with finite simple graphs that generalize the classical independence complex. For a graph $G$ and an integer $t \ge…
For a simplicial complex $\Delta$, we introduce a simplicial complex attached to $\Delta$, called the expansion of $\Delta$, which is a natural generalization of the notion of expansion in graph theory. We are interested in knowing how the…
We find a remarkable family of $\mathrm{G}_2$ structures defined on certain principal $\mathrm{SO}(3)$-bundles $P_\pm\longrightarrow M$ associated with any given oriented Riemannian 4-manifold $M$. Such structures are always cocalibrated.…
The degeneracy of energy levels in a quantum dot of Hall fluid, leading to conductance peaks, can be readily derived from the partition functions of conformal field theory. Their complete expressions can be found for Hall states with both…
The goal of this paper is to set up an obstruction theory in the context of algebras over an operad and in the framework of differential graded modules over a field. Precisely, the problem we consider is the following: Suppose given two…