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arXiv · 0708.3261

Complex Structures on Principal Bundles

Martin Laubinger
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Abstract

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=Σis a closed Riemann surface, there is a correspondence between holomorphic principal G-bundles over Σand coadjoint orbits in the dual of a central extension of the Lie algebra C^\infty(Σ, \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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Martin Laubinger. 2007-08-23. Complex Structures on Principal Bundles. https://arxiv.org/abs/0708.3261

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