We semiclassicalise the theory of quantum group principal bundles to level Poisson geometry. The total space X is a manifold with Poisson-compatible contravariant connection, fibre Poisson-Lie in sense Drinfeld bicovariant and base has an inherited structure connection. latter are known be semiclassical data for differential calculus. illustrated by q-Hopf fibration on standard q-sphere. also c...

We show how to make precise the vague idea that for compact metric spaces that are close together for Gromov– Hausdorff distance, suitable vector bundles on one metric space will have counterpart vector bundles on the other. Our approach employs the Lipschitz constants of projection-valued functions that determine vector bundles. We develop some computational techniques, and we illustrate our i...

Parties in financial markets, industries, compensation design or politics may negotiate on either a piecemeal or a bundled basis. Little is known about the desirability of bundling when values are common and/or information endogenous. The paper shows that bundling encourages information-equalizing investments, thereby facilitating trade. It accordingly revisits and qualifies existing knowledge ...

This paper concerns the moduli spaces of rank two parabolic Higgs bundles and parabolic K(D) pairs over a smooth curve. Precisely which parabolic bundles occur in stable K(D) pairs and stable Higgs bundles is determined. Using Morse theory, the moduli space of parabolic Higgs bundles is shown to be a noncompact, connected, simply connected manifold, and a computation of its Poincaré polynomial ...

We study the Verlinde bundles of generalized theta functions constructed from moduli spaces of sheaves over abelian surfaces. In degree 0, the splitting type of these bundles is expressed in terms of indecomposable semihomogeneous factors. Furthermore, Fourier-Mukai symmetries of the Verlinde bundles are found, consistently with strange duality. Along the way, a transformation formula for the t...

Let X be a smooth projective complex variety with an ample line bundle L, and let D be a simple normal crossing divisor. We establish the Kobayashi-Hitchin correspondence between tame harmonic bundles on X −D and μL-stable parabolic λ-flat bundles with trivial characteristic numbers on (X,D). Especially, we obtain the quasiprojective version of the Corlette-Simpson correspondence between flat b...