Related papers: Pushforwards and Gauge Transformations for Categor…

We consider here the category of diffeological vector pseudo-bundles, and study a possible extension of classical differential geometric tools on finite dimensional vector bundles, namely, the group of automorphisms, the frame bundle, the…

Local connection forms provide a very useful tool for handling connections on principal bundles, because they ignore any complexities of the total space and, essentially, involve only two fundamental features of the structure group, namely…

The standard covariant differentiation procedure for fields in vector bundles is generalised so as to be applicable to fields in general nonaffine bundles in which the fibres may have an arbitrary nonlinear structure. In addition to the…

We introduce a category of noncommutative bundles. To establish geometry in this category we construct suitable noncommutative differential calculi on these bundles and study their basic properties. Furthermore we define the notion of a…

We construct a canonical correspondence from a wide class of reproducing kernels on infinite-dimensional Hermitian vector bundles to linear connections on these bundles. The linear connection in question is obtained through a pull-back…

This note addresses the construction of a notion of parallel transport along superpaths arising from the concept of a superconnection on a vector bundle over a manifold $M$. A superpath in $M$ is, loosely speaking, a path in $M$ together…

In this article we study modules over wild canonical algebras which correspond to extension bundles [9] over weighted projective lines. We prove that all modules attached to extension bundles can be established by matrices with coefficients…

In this article we study the construction of characteristic classes for principal $G$-bundles equipped with an additional structure called transitionally commutative structure (TC structure). These structures classify, up to homotopy,…

Transformational music theory mainly deals with group and group actions on sets, which are usually constituted by chords. For example, neo-Riemannian theory uses the dihedral group D24 to study transformations between major and minor…

The general purpose bitensorially gauge-covariant differentiation procedure set up in the preceding article is specialised to the particular case of bundles with nonlinear fibres that are endowed with a torsion free Riemannian or…

It is shown that the principle of locality and noncommutative geometry can be connnected by a sheaf theoretical method. In this framework quantum spaces are introduced and examples in mathematical physics are given. With the language of…

In the framework of Abstract Differential Geometry, we show that to a given principal sheaf and a representation of its stuctural sheaf in $A^n$, where A is a sheaf of associative, commutative, unital algebras (over R or C), we associate a…

We determine those maps between affine or projective spaces that are linear in the abstract sense of transforming collinear points into collinear points and whose restriction to any line is constant or injective. Our results are extensions…

Motivated by positive energy representations, we classify those continuous central extensions of the compactly supported gauge Lie algebra that are covariant under a 1-parameter group of transformations of the base manifold.

We develop a categorical approach to quivers and their modules. Naturally this leads to a notion of an action of a monoidal category on quivers. Using this, we construct for a large class of quivers rigid monoidal structures on their…

We study classical structures in various categories of completely positive morphisms: on sets and relations, on cobordisms, on a free dagger compact category, and on Hilbert spaces. As an application, we prove that quantum maps with…

We will introduce formal frames of manifolds, which are a generalization of ordinary frames. Their fundamental properties are discussed. In particular, canonical forms are introduced, and torsions are defined in terms of them as a…

We discuss some aspects of heterotic-Type I duality. We focus on toroidal compactification, with special attention for the topology of the gauge group, and the topology of the bundle. We review the arguments leading to a classification of…

We prove that the forgetful morphism from the moduli space of orthogonal bundles to the moduli space of vector bundles over a smooth curve is an embedding. Our proof relies on an explicit description of a set of generators for the…

We consider the problem of existence of representations of topological groupoids on a principal bundle and the classification of such representations up to gauge transformation. Such representations naturally occur in various contexts such…