Related papers: Coarse Bundles
A stratified space is a kind of topological space together with a partition into smooth manifolds. These kinds of spaces naturally arise in the study of singular algebraic varieties, symplectic reduction, and differentiable stacks. In this…
Affine metrics and its associated algebroid bundle are developed. Theses structures are applied to the general relativity and provide an structure for unification of gravity and electromagnetism. The final result is a field equation on the…
Quasi-trees generalize trees in that the unique "path" between two nodes may be infinite and have any countable order type. They are used to define the rank-width of a countable graph in such a way that it is equal to the least upper-bound…
Between the category of exact metric spaces with bounded geometry (about which much is known) and the larger category of arbitrary exact metric spaces (about which little is known) lies the intermediate category of asymptotically exact…
A constructive approach to differential calculus on quantum principal bundles is presented. The calculus on the bundle is built in an intrinsic manner, starting from given graded (differential) *-algebras representing horizontal forms on…
We define and study a simplicial complex which is a homogeneous space for the group $PGL(2, K)$ over a two-dimensional local field $K$. The complex is a generalization of the tree studied by F. Bruhat, J. Tits, J.-P. Serre and P. Cartier in…
The concept of generalised (in the sense of Colombeau) connection on a principal fibre bundle is introduced. This definition is then used to extend results concerning the geometry of principal fibre bundles to those that only have a…
We introduce a notion of coarse embedding at infinity into Hilbert space for metric spaces, which is a weakening of the notion of fibred coarse embedding and a far generalization of Gromov's concept of coarse embedding. It turns out that a…
Algebraic parabolic bundles on smooth projective curves over algebraically closed field of positive characteristic is defined. It is shown that the category of algebraic parabolic bundles is equivalent to the category of orbifold bundles…
Koszul algebras with quadratic Groebner bases, called strong Koszul algebras, are studied. We introduce affine algebraic varieties whose points are in one-to-one correspondence with certain strong Koszul algebras and we investigate the…
In classical field theory, the composite fibred manifolds Y -> Z -> X provides the adequate mathematical formulation of gauge models with broken symmetries, e.g., the gauge gravitation theory. This work is devoted to connections on…
A Steiner bundle is a vector bundle on projective space arising as the cokernel of the map defined by a matrix of linear forms. These come up in various geometric settings, and by now they are the subject of a considerable literature.…
The notion of global higher-form symmetries has received much attention, but leaves room for a more systematic mathematical formulation. In this article, we highlight the concept of higher automorphism bundles from the field of higher…
In this paper we define a Poisson structure on some moduli spaces related to principal G-bundles on elliptic curves, the simplest example being the moduli space of stable pairs: a vector bundle and its global section. We also study…
We develop a ready-to-use comprehensive theory for (super) 2-vector bundles over smooth manifolds. It is based on the bicategory of (super) algebras, bimodules, and intertwiners as a model for 2-vector spaces. We discuss symmetric monoidal…
A vector bundle on a smooth projective variety, if it is generically generated by global sections, yields a rational map to a Grassmannian, called Kodaira map. We investigate the asymptotic behaviour of the Kodaira maps for the symmetric…
We develop a generalized field space geometry for higher-derivative scalar field theories, expressing scattering amplitudes in terms of a covariant geometry on the all-order jet bundle. The incorporation of spacetime and field derivative…
We study gauge symmetry in F-theory in light of global aspects. For this, we consider not only a simple (local) group, but also a semi-simple group with Abelian factors. Once we specify the complete gauge group by decomposing the…
We define double principal bundles (DPBs), for which the frame bundle of a double vector bundle, double Lie groups and double homogeneous spaces are basic examples. It is shown that a double vector bundle can be realized as the associated…
In a previous paper we have introduced the notion of geometric directional bundle of a singular space, in order to introduce global bi-Lipschitz invariants. Then we have posed the question of whether or not the geometric directional bundle…