Related papers: Chains on suspension spectra
In this paper we introduce a method which allows us to study properties of the random uniform simplicial complex. That is, we assign equal probability to all simplicial complexes with a given number of vertices and then consider properties…
Operadic tangent cohomology generalizes the existing cohomology theories of Chevalley--Eilenberg, Hochschild, and Harrison to address the deformation theory of general types of algebras through gadgets known as deformation complexes. The…
We prove that the homological and Balmer spectra in tensor-triangular geometry are functorial in certain definable functors, thereby providing an alternative perspective on functoriality in tensor-triangular geometry from the viewpoint of…
We investigate the similarities between adic finiteness and homological finiteness for chain complexes over a commutative noetherian ring. In particular, we extend the isomorphism properties of certain natural morphisms from homologically…
In this paper we study the cohomology of the de Rham complex of sheaves of reflexive differential forms on a normal complex space. First, we prove that the complex is exact in degree one under suitable conditions on the underlying…
We apply the method of spectral sequences to study classical problems in analysis. We illustrate the method by finding polynomial vector fields that commute with a given polynomial vector field and finding integrals of polynomial…
Some rigorous results can be derived using a very simple approach to hadron spectroscopy, in which a static potential is associated with non-relativistic kinematics. Several regularities of the experimental spectrum are explained by such…
We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…
The purpose of this article is the study of the symmetries in a circular and linear harmonic oscillator chains system, and consequently use them as a means to find the eigenvalues of these configurations. Furthermore, a hidden…
Simplicial homology is a classical tool that assigns a sequence of modules to a simplicial complex, providing invariants for the study of its topological properties. In this article, we introduce the notion of L-fuzzy simplicial homology, a…
Let $X$ be a scheme. In this text, we extend the known definitions of a topology on the set $X(R)$ of $R$-rational points from topological fields, local rings and ad\`ele rings to any ring $R$ with a topology. This definition is functorial…
Using the random complexes of Linial and Meshulam, we exhibit a large family of simplicial complexes for which, whenever affinely embedded into Euclidean space, the filling areas of simplicial cycles is greatly distorted. This phenomenon…
We consider simplicial complexes that are generated from the binomial random 3-uniform hypergraph by taking the downward-closure. We determine when this simplicial complex is homologically connected, meaning that its zero-th and first…
This paper extends results of Hatcher and Vogtmann's work "Cerf Theory for Graphs" to ribbon graphs. Given an orientable, punctured and basepointed surface Sigma, we prove that the space of ribbon graphs that can be drawn in Sigma is…
New bounds are derived for the eigenvalues of sums of Kronecker products of square matrices by relating the corresponding matrix expressions to the covariance structure of suitable bi-linear stochastic systems in discrete and continuous…
Using the spectral theorem for symmetric matrices over a real closed field, we give a quick answer to a problem of Godsil and Sun on degree-similarity of graphs.
Using Dugger's construction of universal model categories, we produce replacements for simplicial and combinatorial symmetric monoidal model categories with better operadic properties. Namely, these replacements admit a model structure on…
New constructions in group homology allow us to manufacture high-dimensional manifolds with controlled simplicial volume. We prove that for every dimension bigger than 3 the set of simplicial volumes of orientable closed connected manifolds…
We study the homology of the dual de Rham complex as functors on the category of abelian groups. We give a description of homology of the dual de Rham complex up to degree 7 for free abelian groups and present a corrected version of the…
We show that Sullivan's model of rational differential forms on a simplicial set $X$ may be interpreted as a (kind of) $0|1$-dimensional supersymmetric quantum field theory over $X$, and, as a consequence, concordance classes of such…