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# Connections on a Parabolic Principal Bundle, II

Published:2009-06-01
Printed: Jun 2009
• Indranil Biswas
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## Abstract

In \emph{Connections on a parabolic principal bundle over a curve, I} 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 the above article 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 generalizes 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.
 Keywords: Parabolic bundle, Atiyah exact sequence, connection
 MSC Classifications: 32L05 - Holomorphic bundles and generalizations 14F05 - Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]

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