Witten couples the open topological B-model to a holomorphic vector bundle by adding to the boundary of the worldsheet a Wilson loop for an integrable connection on the bundle. Using the descent procedure for boundary vertex operators in this context, I generalize this construction to write a worldsheet coupling for a graded vector bundle with an integrable superconnection. I then compute the o...

We define a notion of morphism for quotient vector bundles that yields both a category QVBun and a contravariant global sections functor C : QVBun → Vect whose restriction to trivial vector bundles with fiber F coincides with the contravariant functor Top → Vect of F -valued continuous functions. Based on this we obtain a linear extension of the adjunction between the categories of topological ...

We prove that the Cuntz-Pimsner algebra OE of a vector bundle E of rank ≥ 2 over a compact metrizable space X is determined up to an isomorphism of C(X)algebras by the ideal (1 − [E])K(X) of the K-theory ring K(X). Moreover, if E and F are vector bundles of rank ≥ 2, then a unital embedding of C(X)-algebras OE ⊂ OF exists if and only if 1 − [E] is divisible by 1 − [F ] in the ring K(X). We intr...

Consider a fiber bundle in which the total space, the base space and the fiber are all symplectic manifolds. We study the relations between the quantization of these spaces. In particular, we discuss the geometric quantization of a vector bundle, as oppose to a line bundle, over the base space that recovers the standard geometric quantization of the total space.

The general problem for consistency between arbitrary transports along paths in fibre bundles and bundle morphisms between them is formulated and investigated. The special case of one fibre bundle, its morphism and transport along paths acting in it is considered. The consistency between linear transports along paths in a vector bundle and a Hermitian structure in it is studied.

the geometry of a system of second order differential equations is the geometry of a semispray, which is a globally defined vector field on tm. the metrizability of a given semispray is of special importance. in this paper, the metric associated with the semispray s is applied in order to study some types of foliations on the tangent bundle which are compatible with sode structure. indeed, suff...

Let X be a nonsingular algebraic curve of genus g ≥ 3, and let M ξ denote the moduli space of stable vector bundles of rank n ≥ 2 and degree d with fixed determinant ξ over X such that n and d are coprime and d > n(2g − 2). We assume that if g = 3 then n ≥ 4 and if g = 4 then n ≥ 3. Let W ξ (L) denote the vector bundle over M ξ defined by the direct image p M ξ * (U ξ ⊗ p * X L) where U ξ is a ...

This paper presents a new approach to constructing a meromorphic bundle map between flat vector bundles over a compact Riemann surface having a prescribed Weil divisor (i.e. having prescribed zeros and poles with directional as well as multiplicity information included in the vector case). This new formalism unifies the earlier approach of Ball-Clancey (in the setting of trivial bundles over an...

Let XR be a geometrically irreducible smooth projective curve, defined over R, such that XR does not have any real points. Let X = XR×R C be the complex curve. We show that there is a universal real algebraic line bundle over XR × Pic d(XR) if and only if χ(L) is odd for L ∈ Picd(XR). There is a universal quaternionic algebraic line bundle over X × Pic(X) if and only if the degree d is odd. Tak...

We consider when a smooth vector bundle endowed with a connection possesses non-trivial, local parallel sections. This is accomplished by means of a derived flag of subsets of the bundle. The procedure is algebraic and rests upon the Frobenius Theorem.