Gromov’s Oka Principle, Fiber Bundles and the Conformal Module

A Characterization of the Infinitesimal Conformal Transformations on Tangent Bundles

An Oka Principle for Stein G-manifolds

Let G be a reductive complex Lie group acting holomorphically on Stein manifolds X and Y . Let pX : X → QX and pY : Y → QY be the quotient mappings. Assume that we have a biholomorphism Q := QX → QY and an open cover {Ui} of Q and G-biholomorphisms Φi : p −1 X (Ui)→ p −1 Y (Ui) inducing the identity on Ui. There is a sheaf of groups A on Q such that the isomorphism classes of all possible Y is ...

a characterization of the infinitesimal conformal transformations on tangent bundles

Fiber bundles and Lie algebras of top spaces

In this paper, by using of Frobenius theorem a relation between Lie subalgebras of the Lie algebra of a top space T and Lie subgroups of T(as a Lie group) is determined. As a result we can consider these spaces by their Lie algebras. We show that a top space with the finite number of identity elements is a C^{∞} principal fiber bundle, by this method we can characterize top spaces.

D-brane Conformal Field Theory and Bundles of Conformal Blocks

Conformal blocks form a system of vector bundles over the moduli space of complex curves with marked points. We discuss various aspects of these bundles. In particular, we present conjectures about the dimensions of sub-bundles. They imply a Verlinde formula for non-simply connected groups like PGL(n, C). We then explain how conformal blocks enter in the construction of conformal field theories...