Connections on a parabolic principal bundle, II
Abstract
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.
Cite
@article{arxiv.math/0702278,
title = {Connections on a parabolic principal bundle, II},
author = {Indranil Biswas},
journal= {arXiv preprint arXiv:math/0702278},
year = {2007}
}
Comments
Canadian Mathematical Bulletin (to appear)