Related papers: Principal Bundles and the Dixmier Douady Class
Quantum affine bundles are quantum principal bundles with affine quantum structure groups. A general theory of quantum affine bundles is presented. In particular, a detailed analysis of differential calculi over these bundles is performed,…
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…
A first step towards a systematic theory of relative line bundles over SUSY-curves is presented. In this paper we deal with the case of relative line bundles over families of ordinary Riemann surfaces. Generalizations of the Gauss-Bonnet…
Using a model for the bundle $\hat{\mathcal F}^2M$ of semi-holonomic second order frames of a manifold $M$ as an extension of the bundle ${\mathcal F}^2M$ of holonomic second order frames of $M$, we introduce in $\hat{\mathcal F}^2M$ a…
Let M be a simply connected Riemannian symmetric space, with at most one flat direction. We show that every Riemannian (or unitary) vector bundle with parallel curvature over M is an associated vector bundle of a canonical principal bundle,…
An approach to gauge theory in the context of locally conformally flat space-time is described. It is discussed how there are a number of natural principal bundles associated with any given locally conformally flat space-time $X$. The…
A brief exposition of the general theory of characteristic classes of quantum principal bundles is given. The theory of quantum characteristic classes incorporates ideas of classical Weil theory into the conceptual framework of…
We study the normal bundles of the exceptional sets of isolated simple small singularities in the higher dimension when the Picard group of the exceptional set is $\mathbb{Z}$ and the normal bundle of it has some good filtration. In…
It is shown that every quantum principal bundle is braided, in the sense that there exists an intrinsic braid operator twisting the functions on the bundle. A detailed algebraic analysis of this operator is performed. In particular, it…
In this paper we deal with algebro-geometrical problems connected with testing S-duality conjecture for super-symmetric Yang-Mills quantum field theories in four dimensions. We describe all field configurations such that beta function…
Quantum principal bundles or principal comodule algebras are re-interpreted as principal bundles within a framework of Synthetic Noncommutative Differential Geometry. More specifically, the notion of a noncommutative principal bundle within…
Tangent category theory is a well-established categorical framework for differential geometry. A long list of fundamental geometric constructions, such as the tangent bundle functor, vector fields, Euclidean spaces, and vector bundles have…
We introduce and examine the notion of principal $\mathbb{Z}_2^n$-bundles, i.e., principal bundles in the category of $\mathbb{Z}_2^n$-manifolds. The latter are higher graded extensions of supermanifolds in which a $\mathbb{Z}_2^n$-grading…
We define functorial isomorphisms of parallel transport along \'etale paths for a class of principal $G$-bundles on a $p$-adic curve. Here $G$ is a connected reductive algebraic group of finite presentation and the considered principal…
We study the fixed points of the universal G-equivariant n-dimensional complex vector bundle and obtain a decomposition formula in terms of twisted equivariant universal complex vector bundles of smaller dimension. We use this decomposition…
We report on the connections between noncommutative principal circle bundles, Pimsner algebras and strongly graded algebras. We illustrate several results with the examples of quantum weighted projective and lens spaces and…
A theory of double affine and special double affine bundles, i.e. differential manifolds with two compatible (special) affine bundle structures, is developed as an affine counterpart of the theory of double vector bundles. The motivation…
We prove a version of Grothendieck's descent theorem on an `enriched' principal fiber bundle, a principal fiber bundle with an action of a larger group scheme. Using this, we prove the isomorphisms of the equivariant Picard and the class…
I discuss several issues concerning the use of string models as unified theories of all interactions. After a short review of gauge coupling unification in the string context, I discuss possible motivations for the construction of $SU(5)$…
We review the concept of a graded bundle, which is a generalisation of a vector bundle, its linearisation, and a double structure of this kind. We then present applications of these structures in geometric mechanics including systems with…