Related papers: Equivariant Principal Bundles over the 2-Sphere

We prove that the space of gauge equivalence classes of U(1)-invariant connections on some SU(2)-principle bundles over the 4-sphere S^4 is weakly homotopy equivalent to a component of the second loop space of the 2-sphere S^2.

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…

We find a remarkable family of $\mathrm{G}_2$ structures defined on certain principal $\mathrm{SO}(3)$-bundles $P_\pm\longrightarrow M$ associated with any given oriented Riemannian 4-manifold $M$. Such structures are always cocalibrated.…

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…

We prove that the real parts of equivariant (but non-invariant) eigenfunctions of generic bundle metrics on nontrivial principal $S^1$ bundles over manifolds of any dimension have connected nodal sets and exactly 2 nodal domains. This…

We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…

If $G$ is a finite group or a torus, it is known that there is an isomorphism between the Grothendieck group of homotopy representations and that of generalized homotopy representations for $G$. We prove that there is such an isomorphism…

We define the equivariant holonomy of an invariant connection on a principal U(1)-bundle. The properties of the ordinary holonomy are generalized to the equivariant setting. In particular, equivariant U(1)-bundles with connection are shown…

In this paper the K-Theory and the category of homogeneous vector bundles on the symplectic Grassmannian SpGr(2,N) of isotropic 2-planes are discussed.

We develop the theory of simplicial extensions for bundle gerbes and their characteristic classes with a view towards studying descent problems and equivariance for bundle gerbes. Equivariant bundle gerbes are important in the study of…

For the universal isomonodromic deformation of an irreducible logarithmic rank two connection over a smooth complex projective curve of genus at least two, consider the family of holomorphic vector bundles over curves underlying this…

Let $G$ be a compact connected Lie group and let $\xi,\nu$ be complex vector bundles over the classifying space $BG$. The problem we consider is whether $\xi$ contains a subbundle which is isomorphic to $\nu$. The necessary condition is…

The classification of algebraic vector bundles of rank 2 over smooth affine fourfolds is a notoriously difficult problem. Isomorphism classes of such vector bundles are not uniquely determined by their Chern classes, in contrast to the…

Let (X, \omega) be a compact connected Kaehler manifold of complex dimension d and E_G a holomorphic principal G-bundle on X, where G is a connected reductive linear algebraic group defined over C. Let Z (G) denote the center of G. We prove…

We study a natural map from representations of a free (resp. free abelian) group of rank g in GL_r(C), to holomorphic vector bundles of degree zero over a compact Riemann surface X of genus g (resp. complex torus X of dimension g). This map…

We show that isomorphism classes $[\mathcal{A}]$ of flat $q\times q$ matrix bundles $\mathcal{A}$ (or projectively flat rank-$q$ complex vector bundles $\mathcal{E}$) on a pro-torus $\mathbb{T}$ are in bijective correspondence with the…

In this paper, we classify the homotopy types of the total spaces of $S^{2k-1}$-bundles (or fibrations) over $S^{2k}$ for $2\leq k\leq 6$. One of the two key new ingredients in the argument is the new necessary and sufficient conditions for…

In this paper we proof the existence of a linearization for singular principal G-bundles not depending on the base curve. This allow us to construct the relative compact moduli space of {\delta}-(semi)stable singular principal G-bundles…

The theory of principal bundles makes sense in any infinity-topos, such as that of topological, of smooth, or of otherwise geometric infinity-groupoids/infinity-stacks, and more generally in slices of these. It provides a natural geometric…

Let $\Gamma$ be a finite group acting on a Lie group $G$. We consider a class of group extensions $1 \to G \to \hat{G} \to \Gamma \to 1$ defined by this action and a $2$-cocycle of $\Gamma$ with values in the centre of $G$. We establish and…