Related papers: Double vector bundles and duality

It is known that the T-dual of a circle bundle with H-flux (given by a Neveu-Schwarz 3-form) is the T-dual circle bundle with dual H-flux. However, it is also known that torus bundles with H-flux do not necessarily have a T-dual which is a…

This paper is devoted to the study of the family of morphisms of vector bundle, defined by the systems equivalence to linear differential equations. It is proved, that the specified families of the morphisms of vector bundle is not…

In this paper we study T-duality for principal torus bundles with H-flux. We identify a subset of fluxes which are T-dualizable, and compute both the dual torus bundle as well as the dual H-flux. We briefly discuss the generalized Gysin…

A noncommutative-geometric formalism of framed principal bundles is sketched, in a special case of quantum bundles (over quantum spaces) possessing classical structure groups. Quantum counterparts of torsion operators and Levi-Civita type…

We completely classify all quotient bundles of a given vector bundle on the Fargues-Fontaine curve. As consequences, we have two additional classification results: a complete classification of all vector bundles that are generated by a…

In this note we make use of some properties of vector fields on a manifold to give an alternate proof to [3] for the equivalence between connections and parallel transport on vector bundles over manifolds. Out of the proof will emerge a new…

We define a turning of a rank-$2k$ vector bundle $E \to B$ to be a homotopy of bundle automorphisms $\psi_t$ from $\mathbb{Id}_E$, the identity of $E$, to $-\mathbb{Id}_E$, minus the identity, and call a pair $(E, \psi_t)$ a turned bundle.…

A plane curve C defined by a homogeneous polynomial satisfying Laplace's equation appears canonically as the vanishing of the Pfaffian of a skew-symmetric matrix of linear forms. As a consequence there is a natural semi-stable rank two…

We present the notion of a filtered bundle as a generalisation of a graded bundle. In particular, we weaken the necessity of the transformation laws for local coordinates to exactly respect the weight of the coordinates by allowing more…

We define a subcategory of the category of diffeological spaces, which contains smooth manifolds, the diffeomorphism subgroups and its coadjoint orbits. In these spaces we construct a tangent bundle, vector fields and a de Rham cohomology.

An overview about C*-algebra bundles with a Z-grading is presented, with particular emphasis on classification questions. In particular, we discuss the role of the representable KK(X ; -, -)-bifunctor introduced by Kasparov. As an…

In this paper, we explain how the abstract notion of a differential bundle in a tangent category provides a new way of thinking about the category of modules over a commutative ring and its opposite category. MacAdam previously showed that…

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…

We review the concept of a graded bundle as a natural generalisation of a vector bundle. Such geometries are particularly nice examples of more general graded manifolds. With hindsight there are many examples of graded bundles that appear…

We provide a pedagogical introduction to the theory of principal 2-bundles with adjusted connections and show how they enter the description of geometric and non-geometric T-dualities as proposed in arXiv:2204.01783. This description…

We give a short proof of the Gauss-Bonnet theorem for a real oriented Riemannian vector bundle $E$ of even rank over a closed compact orientable manifold $M$. This theorem reduces to the classical Gauss-Bonnet-Chern theorem in the special…

We study vector bundles on the moduli stack of elliptic curves over a local ring R. If R is a field or a discrete valuation ring of (residue) characteristic not 2 or 3, all these vector bundles are sums of line bundles. For R the 3-local…

In this paper we develop the geometry of bounded Fr\'echet manifolds. We prove that a bounded Fr\'echet tangent bundle admits a vector bundle structure. But the second order tangent bundle $T^2M$ of a bounded Fr\'echet manifold $M$, becomes…

We describe categories of equivariant vector bundles on certain toroidal spherical varieties in linear algebra terms: vector spaces equipped with filtrations, group and Lie algebra actions, and linear maps preserving these structures.

This article studies the harmonicity of vector fields on Riemannian manifolds, viewed as maps into the tangent bundle equipped with a family of Riemannian metrics. Geometric and topological rigidity conditions are obtained, especially for…