Complex Structures on Principal Bundles

Details Complex Structures on Principal Bundles Complex Structures on Principal Bundles

2007-08-23

arxiv.org/abs/0708.3261v1

Mathematics

Differential Geometry

17 pages

Scientific paper

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 G-bundles over \Sigma and coadjoint orbits in the dual of a central extension of the Lie algebra C^\infty(\Sigma, \g). We review these results and provide the details of an integrability condition for almost complex structures on smoothly trivial bundles. This article is a shortened version of the author's Diplom thesis.

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