Related papers: Invitation to higher local fields, Part I, section…

This article is part introduction and part survey to the mathematical area centered around local cohomology.

Many active mathematical research topics nowadays include the concepts of valued fields and local fields, especially the local field of p-adic numbers Qp and the field of formal Laurent series F((X)). Local fields are a notion situated in…

We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…

It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories with n> 1. Recently the physical meaning of these higher categorical…

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…

This work is a survey of relations between Drinfeld modules and higher dimensional fields of positive characteristic. The main new result stated is the expression of vanishing orders of certain modular forms through partial zeta values.

Topological conformal field theories are defined using only basic results from the theory of quasiconformal mappings.

For an arbitrary field p-torsion and cotorsion of the Milnor groups K_n(F) and K_n^{t}(F)=K_n(F)/\cap_{l\ge1} lK_n(F) are discussed. The work contains further discussions of an analogue of Satz 90 for K_n(F) and K_n^{t}(F) and computation…

This is a concise survey of links between Galois module theory and class field theory (CFT). It explores various uses of CFT in Galois module theory, it comments on the absence of CFT in contexts where it might be expected to play a role…

This is an introduction to noncommutative local reciprocity maps for totally ramified Galois extensions with arithmetically profinite group. These maps in general are not homomorphisms but Galois cycles; a description of their image and…

This is an introductory article on high dimensional knots for the beginners. High dimensional knot theory is an exciting field. It is a field of knot theory, which is one of topology and is connected with many ones. In this article we use…

This expository paper explores the interaction of group ordering with topological questions, especially in dimensions 2 and 3. Among the topics considered are surfaces, braid groups, 3-manifolds and their structures such as foliations and…

This is the first chapter in our "Toric Topology" book project. Further chapters are coming. Comments and suggestions are very welcome.

These notes are an expanded version of an introductory lecture on contact geometry given at the 2001 Georgia Topology Conference. They are intended to present some of the "topological" aspects of three dimensional contact geometry.

Multi-material structural topology and shape optimization problems are formulated within a phase field approach. First-order conditions are stated and the relation of the necessary conditions to classical shape derivatives are discussed. An…

This work sketches the author classification of complete discrete valuation fields K of characteristic 0 with residue field of characteristic p into two classes depending on the behaviour of the torsion part of a differential module. For…

We present a general formalism for higher dimensional versions of lattice gauge fields based on higher strict homotopy groupoids. First, using the language of nonabelian Algebraic Topology, we define local lattice higher gauge fields. Then,…

A category which generalises to higher dimensions many of the features of the Temperley-Lieb category is introduced.

An exponential homomorphism for a complete discrete valuation field of characteristic zero which relates differential forms and the Milnor K-groups of the field is studied. An application to explicit formulas is included.

We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. Starting from ZFC, the exposition in this first part includes relation and order theory as well as a construction of…