Related papers: Principaloid bundles

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 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.

We investigate principal $G$-bundles on a compact K\"ahler manifold, where $G$ is a complex algebraic group such that the connected component of it containing the identity element is reductive. Defining (semi)stability of such bundles, it…

Let $M$ be a compact connected special flat affine manifold without boundary equipped with a Gauduchon metric $g$ and a covariant constant volume form. Let $G$ be either a connected reductive complex linear algebraic group or the real locus…

The geometry of graded principal bundles is discussed in the framework of graded manifold theory of Kostant-Berezin-Leites. In particular, we prove that a graded principal bundle is globally trivial if and only if it admits a global graded…

Holomorphic principal G-bundles over a complex manifold M can be studied using non-abelian cohomology groups H^1(M,G). On the other hand, if M=\Sigma is a closed Riemann surface, there is a correspondence between holomorphic principal…

The aim of this paper is to review and discuss in detail local aspects of principal bundles with groupoid structure. Many results, in particular from the second and third section, are already known to some extents, but, due to the lack of a…

We consider principal bundles over homogeneous spaces G/P, where P is a parabolic subgroup of a semisimple and simply connected complex linear algebraic group G. We prove that a holomorphic principal H--bundle, where H is a complex…

We introduce a general definition of higher-form connections on principal $\infty$-bundles in differential geometry. This is achieved by developing the formal differentiation and integration of maps from smooth manifolds to derived stacks…

Let $g$ be locally homogeneous (LH) Riemannian metric on a differentiable compact manifold $M$, and $K$ be a compact Lie group endowed with an $\mathrm {ad}$-invariant inner product on its Lie algebra $\mathfrak{k}$. A connection $A$ on a…

The purpose of this paper is to propose a sheaf theoretic approach to the theory of quantum principal bundles over non affine bases. We study the quantization of principal bundles G -> G/P, where G is a semisimple group and P a parabolic…

Let $H$ be a connected semisimple linear algebraic group defined over $\mathbb C$ and $X$ a compact connected Riemann surface of genus at least three. Let ${\mathcal M}'_X(H)$ be the moduli space parametrising all topologically trivial…

Two hierarchies of quantum principal bundles over quantum real projective spaces are constructed. One hierarchy contains bundles with U(1) as a structure group, the other has the quantum group $SU_q(2)$ as a fibre. Both hierarchies are…

The motivation for this paper stems \cite{CR} from the need to construct explicit isomorphisms of (possibly nontrivial) principal $G$-bundles on the space of loops or, more generally, of paths in some manifold $M$, over which I consider 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,…

In this paper we construct certain moduli spaces, which we call moduli spaces of (principal) $F$-bundles, and study their basic properties. These spaces are associated to triples consisting of a smooth projective geometrically connected…

We propose a generalisation of the notion of associated bundles to a principal bundle constructed via group action cocycles rather than via mere representations of the structure group. We devise a notion of connection generalising Ehresmann…

Let $G$ be a Lie group and $G\to\Aut(G)$ be the canonical group homomorphism induced by the adjoint action of a group on itself. We give an explicit description of a 1-1 correspondence between Morita equivalence classes of, on the one hand,…

In this note, we introduce the notion of a singular principal G-bundle, associated to a reductive algebraic group G over the complex numbers by means of a faithful representation $\varrho^\p\colon G\lra \SL(V)$. This concept is meant to…

By virtue of the well-known theorem, a structure Lie group G of a principal bundle P is reducible to its closed subgroup H iff there exists a global section of the quotient bundle P/H. In gauge theory, such sections are treated as classical…