Related papers: Note on generalised connections and affine bundles
There are two ways to unify gravitational field and gauge field. One is to represent gravitational field as principal bundle connection, and the other is to represent gauge field as affine connection. Poincar\'{e} gauge theory and…
A broader definition of generalized truncations of graphs is introduced followed by an exploration of some standard concepts and parameters with regard to generalized truncations.
We introduce and study a generalized concept of boundedness of a subset of a normed vector space with respect to a cone, which is defined as lower boundedness of the images of the underlying set through all the positive functionals of the…
This work revisits, from a geometric perspective, the notion of discrete connection on a principal bundle, introduced by M. Leok, J. Marsden and A. Weinstein. It provides precise definitions of discrete connection, discrete connection form…
We investigate principal bundles over a root stack. In case of dimension one, we generalize the criterion of Weil and Atiyah for a principal bundle to have an algebraic connection.
In the paper, we introduce the terminology equivariant pointwise clutching map. By using this, we give details on how to glue an equivariant vector bundle over a finite set so as to obtain a new Lie group representation such that the…
A new concept called multilevel contours is introduced through this article by the author. Theorems on contours constructed on a bundle of complex planes are stated and proved. Multilevel contours can transport information from one complex…
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 study a type of connection forms, given by Chen integrals, over pathspaces by placing such forms within a category-theoretic framework of principal bundles and connections. We introduce a notion of 'decorated' principal bundles, develop…
The group of vertical diffeomorphisms of a principal bundle forms the generalised action Lie groupoid associated to the bundle. The former is generated by the group of maps with value in the structure group, which is also the group of…
Any leafwise connection on a fibre bundle over a foliated manifold is proved to come from a connection on this fibre bundle.
We give a survey on projective ring lines and some of their substructures which in turn are more general than a projective line over a ring.
Motivated by the computations done in \cite{C1}, where I introduced and discussed what I called the groupoid of generalized gauge transformations, viewed as a groupoid over the objects of the category $\mathsf{Bun}_{G,M}$ of principal…
We propose here a multidimensional generalisation of the notion of link introduced in our previous papers and we discuss some consequences for simplicial measures and sums of function algebras.
In this paper, we overview one promising avenue of progress at the mathematical foundation of deep learning: the connection between deep networks and function approximation by affine splines (continuous piecewise linear functions in…
We investigate the relative logarithmic connections on a holomorphic vector bundle over a complex analytic family. We give a sufficient condition for the existence of a relative logarithmic connection on a holomorphic vector bundle singular…
The main aim of this paper is to generalize the concept of vector space by the hyperstructure. We generalize some definitions such as hypersubspaces, linear combination, Hamel basis, linearly dependence and linearly independence. A few…
We compare two notions of $G$-fiber bundles and $G$-principal bundles in the literature, with an aim to clarify early results in equivariant bundle theory that are needed in current work of equivariant algebraic topology. We also give…
The aim of this paper is to study the characteristics of a general method to produce a new approximation sequence from a given one, by using suitable convex combinations.
For a smooth manifold $M$, it was shown in \cite{BPH} that every affine connection on the tangent bundle $TM$ naturally gives rise to covariant differentiation of multivector fields (MVFs) and differential forms along MVFs. In this paper,…