相关论文: Ehreshmann theory of connection in a principal bun…

These lectures notes contain an introduction to General Relativity. They are addressed to a general mathematical audience with no specific background in physics. The goal is to motivate and explain Einstein's theory of gravity and discuss…

Let $\mathbb{X}=[X_1\rightrightarrows X_0]$ be a Lie groupoid equipped with a connection, given by a smooth distribution $\mathcal{H} \subset T X_1$ transversal to the fibers of the source map. Under the assumption that the distribution…

A class of models intended to be as minimal and structureless as possible is introduced. Even in cases with simple rules, rich and complex behavior is found to emerge, and striking correspondences to some important core known features of…

We discuss the possibility of making the {\it initial} definitions of mutually different (possibly interacting, or even entangled) systems in the context of decoherence theory. We point out relativity of the concept of elementary physical…

For a smooth (locally trivial) principal bundle in Ehresmann's sense, the relation between the commuting vertical and horizontal actions of the structural Lie group and the structural Lie groupoid (isomorphisms between vertical fibers) is…

In this note we consider a few interesting properties of discrete connections on principal bundles when the structure group of the bundle is an abelian Lie group. In particular, we show that the discrete connection form and its curvature…

Tangent categories provide an axiomatic approach to key structural aspects of differential geometry that exist not only in the classical category of smooth manifolds but also in algebraic geometry, homological algebra, computer science, and…

We survey some of the connections linking complex dynamics to other fields of mathematics and science. We hope to show that complex dynamics is not just interesting on its own but also has value as an applicable theory.

We provide a geometric interpretation for the connecting homomorphism in the localization sequence of Hermitian $K$-theory. As an application, we compute the Hermitian $K$-theory of projective bundles and Grassmannians in the regular case.…

Quantum theory can be understood as pointing to an ontology of relations. I observe that this reading of quantum mechanics is supported by the ubiquity of relationality in contemporary fundamental physics, including in classical mechanics,…

In the main part of this paper a connection is just a fiber projection onto a (not necessarily integrable) distribution or sub vector bundle of the tangent bundle. Here curvature is computed via the Froelicher-Nijenhuis bracket, and it is…

This paper is a very brief introduction to knot theory. It describes knot coloring by quandles, the fundamental group of a knot complement, and handle-decompositions of knot complements.

Network theory provides tools which are particularly appropriate for assessing the complex interdependencies that characterise our modern connected world. This article presents an introduction to network theory, in a way that doesn't…

The paper presents a classification theorem for the class of flat connections with triangular (0,1)-components on a topologically trivial complex vector bundle over a compact Kahler manifold. As a consequence we obtain several results on…

Extended spinor connections associated with composite spin-tensorial bundles are considered. Commutation relationships for covariant and multivariate differentiations and corresponding curvature spin-tensors are derived.

A new formulation of what may be called the "fundamental theorem of the theory of relativity" is presented and proved in (3+1)-space-time, based on the full classification of special transformations and the corresponding velocity addition…

This book is a manual for the course of electrodynamics and theory of relativity. It is recommended primarily for students of mathematical departments. This defines its style: I use elements of vectorial and tensorial analysis, differential…

This short note gives an overview of how a few conjectures and theorems of the author and collaborators fit together. It was prepared for Oberwolfach's workshop Differentialgeometrie im Gro{\ss}en, 28 June - 4 July 2015, and contains no new…

In this paper, we consider a generalization of the theory of Higgs bundles over a smooth complex projective curve in which the twisting of the Higgs field by the canonical bundle of the curve is replaced by a rank 2 vector bundle. We define…

A review of the parallel transport (translation) in fibre bundles is presented. The connections between transports along paths and parallel transports in fibre bundles are examined. It is proved that the latter ones are special cases of the…