Connections on a parabolic principal bundle, II

Details Connections on a parabolic principal bundle, II Connections on a parabolic principal bundle, II

2007-02-10

arxiv.org/abs/math/0702278v1

Mathematics

Algebraic Geometry

Canadian Mathematical Bulletin (to appear)

Scientific paper

In \cite{Bi2} (Canad. Jour. Math. Vol. 58) we defined connections on a parabolic principal bundle. While connections on usual principal bundles are defined as splittings of the Atiyah exact sequence, it was noted in \cite{Bi2} that the Atiyah exact sequence does not generalize to the parabolic principal bundles. Here we show that a twisted version of the Atiyah exact sequence generalize to the context of parabolic principal bundles. For usual principal bundles, giving a splitting of this twisted Atiyah exact sequence is equivalent to giving a splitting of the Atiyah exact sequence. Connections on a parabolic principal bundle can be defined using the generalization of the twisted Atiyah exact sequence.

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