Related papers: An introduction to higher dimensional local fields…
This is an introduction to Grothendieck's descent theory, with some stress on the general machinery of fibered categories and stacks.
We introduce a topology, which we call the regional topology, on the space of all real functions on a given locally compact metric space. Next we obtain a new versions of Schauder's fixed point theorem and Ascoli's theorem. We use these…
A new and extensive formalism is developed for monads and galaxies in non-standard enlargements. It is shown that monads and galaxies can be manipulated using order-preserving and order-reversing set-to-set maps, and that set properties…
This purpose of this book is twofold: to provide a general introduction to higher category theory (using the formalism of "quasicategories" or "weak Kan complexes"), and to apply this theory to the study of higher versions of Grothendieck…
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
We study the consequences of the presence of a boundary in topological field theories in various dimensions. We characterize, univocally and on very general grounds, the field content and the symmetries of the actions which live on the…
New features are described for models with multi-particle area-dependent potentials, in any number of dimensions. The corresponding many-body field theories are investigated for classical configurations. Some explicit solutions are given,…
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…
We discuss the following topics: n-dimensional local fields and adelic groups; harmonic analysis on local fields and adelic groups for two-dimensional schemes (function spaces, Fourier transform, Poisson formula); representations of…
The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology,…
We review recent results concerning general properties of higher dimensional black holes. The topics selected with particular focus are those concerning topology, symmetry, and uniqueness properties of asymptotically flat vacuum black holes…
The soft topological spaces and some their related concepts have stud- ied in [7]. In this paper, we introduce and study the notions of soft connected topological spaces after a review of preliminary definitions.
Some of the basic concepts of topology are explored through known physics problems. This helps us in two ways, one, in motivating the definitions and the concepts, and two, in showing that topological analysis leads to a clearer…
I discuss the general formalism of two-dimensional topological field theories defined on open-closed oriented Riemann surfaces, starting from an extension of Segal's geometric axioms. Exploiting the topological sewing constraints allows for…
These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories. Introduction. Lecture 1. WDVV equations and Frobenius manifolds. {Appendix A.} Polynomial…
Class field theory furnishes an intrinsic description of the abelian extensions of a number field that is in many cases not of an immediate algorithmic nature. We outline the algorithms available for the explicit computation of such…
This is a survey of motivations, constructions and applications of higher prequantum geometry. In section 1 we highlight the open problem of prequantizing local field theory in a local and gauge invariant way, and we survey how a solution…
Dimensionality is one of the most important properties of complex physical systems. However, only recently this concept has been considered in the context of complex networks. In this paper we further develop the previously introduced…
Topological conformal field theories are defined using only basic results from the theory of quasiconformal mappings.