Related papers: Graded bundles and homogeneity structures

Topological T-duality is a transformation taking a gerbe on a principal torus bundle to a gerbe on a principal dual-torus bundle. We give a new geometric construction of T-dualization, which allows the duality to be extended in following…

A tangent category is a category with an endofunctor, called the tangent bundle functor, which is equipped with various natural transformations that capture essential properties of the classical tangent bundle of smooth manifolds. In this…

In this paper, we introduce a study of prolongations of homogeneous vector bundles. We give an alternative approach for the prolongation. For a given homogeneous vector bundle E, we obtain a new homogeneous vector bundle. The homogeneous…

Jet manifolds and vector bundles allow one to employ tools of differential geometry to study differential equations, for example those arising as equations of motions in physics. They are necessary for a geometrical formulation of…

This review paper is concerned with the generalizations to field theory of the tangent and cotangent structures and bundles that play fundamental roles in the Lagrangian and Hamiltonian formulations of classical mechanics. The paper…

Frame bundles equipped with a principal connection have their local structure characterised by a 1-form, called the Cartan connection 1-form, which gathers the principal connection form and the soldering form. We introduce generalised frame…

A categorical principal bundle is a structure comprised of categories that is analogous to a classical principal bundle; examples arise from geometric contexts involving bundles over path spaces. We show how a categorical principal bundle…

We propose a description of T-duality between general geometric and non-geometric backgrounds as higher groupoid bundles with connections. Our description extends the previous observation by Nikolaus and Waldorf that the topological aspects…

A gauge theory is associated with a principal bundle endowed with a connection permitting to define horizontal lifts of paths. The horizontal lifts of surfaces cannot be defined into a principal bundle structure. An higher gauge theory is…

This paper analyses non-regular $|2|$-graded geometries, and show that they share many of the properties of regular geometries -- the existence of a unique normal Cartan connection encoding the structure, the harmonic curvature as…

Stratifolds are considered from a categorical point of view. We show among others that the category of stratifolds fully faithfully embeds into the category of ${\mathbb R}$-algebras as does the category of smooth manifolds. We prove that a…

We propose a generalization of logarithmic and Schwarzenberger bundles over $\P^n=\P^n(\C)$ when the rank is greater than $n$. The first ones are associated to finite sets of points on $\P^{n\vee}$ and the second ones to curves with degree…

We give a definition of `coherent tangent bundles', which is an intrinsic formulation of wave fronts. In our application of coherent tangent bundles for wave fronts, the first fundamental forms and the third fundamental forms are considered…

Given an arbitrary topological complex vector space $A$, a quotient vector bundle for $A$ is a quotient of a trivial vector bundle $\pi_2:A\times X\to X$ by a fiberwise linear continuous open surjection. We show that this notion subsumes…

The double point relation defines a natural theory of algebraic cobordism for bundles on varieties. We construct a simple basis (over the rationals) of the corresponding cobordism groups over Spec(C) for all dimensions of varieties and…

Motivated by the application problem of sensor fusion the author introduced the concept of graded set. It is reasoned that in classification problem arising in an information system (represented by information table), a novel set called…

In this article we announce some results on compactifying moduli spaces of rank-2 vector bundles on surfaces by spaces of vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so called bubbling of vector…

The Lagrangian description of mechanical systems and the Legendre Transformation (considered as a passage from the Lagrangian to the Hamiltonian formulation of the dynamics) for point-like objects, for which the infinitesimal configuration…

This is a review of the basic concepts of the theory of real and complex smooth vector bundles with finite rank. Besides, the concept of a tensor field is studied within the general framework of a smooth vector bundle rather than a smooth…

We develop a general theory for irreducible homogeneous spaces $M= G/H$, in relation to the nullity $\nu$ of their curvature tensor. We construct natural invariant (different and increasing) distributions associated with the nullity, that…