相关论文: Homological matrices

Various relations between conformal quantum field theories in one, two and four dimensions are explored. The intention is to obtain a better understanding of 4D CFT with the help of methods from lower dimensional CFT.

In this study, we introduce the concept of commutative quaternions and commutative quaternion matrices. Firstly, we give some properties of commutative quaternions and their Hamilton matrices. After that we investigate commutative…

We classify the metric spaces that can be approximated by finite homogeneous ones.

We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…

This is a survey of various types of Floer theories (both in symplectic geometry and gauge theory) and relations among them.

Hexagon relations are combinatorial or algebraic realizations of four-dimensional Pachner moves. We introduce some simple set-theoretic hexagon relations and then `quantize' them using what we call `polynomial hexagon cohomologies'. Based…

We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of…

We define several versions of the cohomology ring of an associative algebra. These ring structures unify some well known operations from homological algebra and differential geometry. They have some formal resemblance with the quantum…

We compute numerically the homology of several graph complexes in low loop orders, extending previous results.

Using Morse theory and a new relative homological linking of pairs, we prove a ``homological linking principle'', thereby generalizing many well known results in critical point theory.

The different notions of matings of pairs of equal degree polynomials are introduced and are related to each other as well as known results on matings. The possible obstructions to matings are identified and related. Moreover the relations…

We define a model for the homology of manifolds and use it to describe the intersection product on the homology of compact oriented manifolds and to define homological quantum field theories which generalizes the notions of string topology…

We use sheaf theory and the six operations to define and study the (equivariant) homology of stacks. The construction makes sense in the algebraic, complex-analytic, or even topological categories.

A quantum deformation of the adjoint action of the special linear group on the variety of nilpotent matrices is introduced. New non-embedded quantum homogeneous spaces are obtained related to certain maximal coadjoint orbits, and known…

In this paper we develope a categorical theory of relations and use this formulation to define the notion of quantization for relations. Categories of relations are defined in the context of symmetric monoidal categories. They are shown to…

In this note, we describe a theory of linked Hom spaces which complements that of linked Grassmannians. Given two chains of vector bundles linked by maps in both directions, we give conditions for the space of homomorphisms from one chain…

We give a rough description of the 'categories' formed by quantum field theories. A few recent mathematical conjectures derived from quantum field theories, some of which are now proven theorems, will be presented in this language.

Homology with values in a connection with possibly irregular singular points on an algebraic curve is defined, generalizing homology with values in the underlying local system for a connection with regular singular points. Integration…

We construct a singular homology theory on the category of schemes of finite type over a Dedekind domain and verify several basic properties. For arithmetic schemes we construct a reciprocity isomorphism between the integral singular…

We define a notion of symmetric monoidal closed (SMC) theory, consisting of a SMC signature augmented with equations, and describe the classifying categories of such theories in terms of proof nets.