Related papers: Buchsbaum* complexes
We provide algorithmic methods to check the Cohen--Macaulayness, Buchsbaumness and/or Gorensteiness of some families of semigroup rings that are constructed from the dilation of bounded convex polyhedrons of $\R^3_{\geq}$. Some families of…
In the paper we treat Gale diagrams in a combinatorial way. The interpretation allows to describe simplicial complexes which are Alexander dual to boundaries of simplicial polytopes and, more generally, to nerve-complexes of general…
We study extensions of double groupoids in the sense of \cite{AN2} and show some classical results of group theory extensions in the case of double groupoids. For it, given a double groupoid $(\mathcal{B}; \mathcal{V},\mathcal{H};…
Scattered over the past few years have been several occurrences of simplicial complexes whose topological behavior characterize the Cohen-Macaulay property for quotients of polynomial rings by arbitrary (not necessarily squarefree) monomial…
In this note we clarify the relation between extended world-sheet supersymmetry and generalized complex structure. The analysis is based on the phase space description of a wide class of sigma models. We point out the natural isomorphism…
This paper makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group which are preserved by automorphisms of the…
We study cubical sets without degeneracies, which we call square sets. These sets arise naturally in a number of settings and they have a beautiful intrinsic geometry; in particular a square set C has an infinite family of associated square…
We calculate the ordinary $C_2$-cohomology, with Burnside ring coefficients, of $BU(2)$, the classifying space for $C_2$-equivariant complex 2-plane bundles, using an extended grading that allows us to capture a more natural set of…
We graph-theoretically characterize the class of graphs $G$ such that $I(G)^2$ are Buchsbaum.
In this paper, we consider hypergraphs whose vertices are distinct points moving smoothly on a Riemannian manifold M. We take these hypergraphs as graded submanifolds of configuration spaces. We construct double complexes of differential…
Let $(X,g)$ be a compact Riemannian stratified space with simple edge singularity. Thus a neighbourhood of the singular stratum is a bundle of truncated cones over a lower dimensional compact smooth manifold. We calculate the various…
Taking the l^1-completion and the topological dual of the singular chain complex gives rise to l^1-homology and bounded cohomology respectively. In contrast to l^1-homology, major structural properties of bounded cohomology are well…
We consider manifolds endowed with a contact pair structure. To such a structure are naturally associated two almost complex structures. If they are both integrable, we call the structure a normal contact pair. We generalize the Morimoto's…
A piecewise constant curvature manifold is a triangulated manifold that is assigned a geometry by specifying lengths of edges and stipulating that for a chosen background geometry (Euclidean, hyperbolic, or spherical), each simplex has an…
We introduce a new model for random simplicial complexes which with high probability generates a complex that has a simply-connected double cover. Hence we develop a model for random simplicial complexes with fundamental group…
We observe that the singular part of the second bounded cohomology group of boundedly simple groups is trivial.
The dual complex of a singularity is defined, up-to homotopy, using resolutions of singularities. In many cases, for instance for isolated singularities, we identify and study a "minimal" representative of the homotopy class that is well…
A numerical characterization is given of the so-called h-triangles of sequentially Cohen-Macaulay simplicial complexes. This result characterizes the number of faces of various dimensions and codimensions in such a complex, generalizing the…
Intersection homology is defined for simplicial, singular and PL chains and it is well known that the three versions are isomorphic for a full filtered simplicial complex. In the literature, the isomorphism, between the singular and the…
We propose a new look on triangulated categories, which is based on the second Hochschild cohomology.