Related papers: An introduction to higher dimensional local fields…
This is an introduction to the basic ideas and to a few further selected topics in conformal quantum field theory and in the theory of Kac-Moody algebras.
The embeddings of complex plane projective curves in the plane are a cornerstone of the topological study of algebraic varieties. In this work, we deal with the local and global aspects of these embeddings, with a special attention to its…
In this paper we propose a naive construction of 2-dimensional extended topological quantum field theories (TQFTs), which can be further generalized to the higher-dimension extended TQFTs.
Action principles of the BF type for diffeomorphism invariant topological field theories living in n-dimensional spacetime manifolds are presented. Their construction is inspired by Cuesta and Montesinos' recent paper where Cartan's first…
The monograph "Invitation to higher local fields" is the result of the conference on higher local fields held in Muenster, August 29 to September 5, 1999. The aim is to provide an introduction to higher local fields (more generally complete…
In this expository paper we introduce extended topological quantum field theories and the cobordism hypothesis.
We adapt the study of hyperspaces and function spaces from classical topology to digital topology. We define digital hyperspaces and digital function graphs, and study some of their relationships and graphical properties.
This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…
Categorial methods for generating new local algebras from old ones are presented. A direct proof of the differential structure of the prolongations of a manifold is proposed.
A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…
An introduction to geography of log models with applications to positive cones of FT varieties and to geometry of minimal models and Mori fibrations.
In this paper, we give a survey of a geometrical theory of Jacobi forms of higher degree. And we present some geometric results and discuss some geometric problems to be investigated in the future.
By the introduction of locally constant prefactorization algebras at a fixed scale, we show a mathematical incarnation of the fact that observables at a given scale of a topological field theory propagate to every scale over euclidean…
We give an overview of differential cohomology from the point of view of algebraic topology. This includes a survey of several different definitions of differential cohomology groups, a discussion of differential characteristic classes, an…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
Mostly aimed at an audience with backgrounds in geometry and homological algebra, these notes offer an introduction to derived geometry based on a lecture course given by the second author. The focus is on derived algebraic geometry, mainly…
Let E be a locally solid vector lattice. In this paper, we consider two particular vector subspaces of the space of all order bounded operators on E. With the aid of two appropriate topologies, we show that under some conditions, they…
In the context of relative topos theory via stacks, we introduce the notion of existential fibred site and of existential topos of such a site. These notions allow us to develop relative topos theory in a way which naturally generalizes the…
Covering-based rough set theory is an extension to classical rough set. The main purpose of this paper is to study covering rough sets from a topological point of view. The relationship among upper approximations based on topological spaces…
In this work, we generalize several topological results and concepts from ring theory to the setting of monoids.