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Connections on a Parabolic Principal Bundle, II |
Canad. Math. Bull. 52(2009), 175-185
Published:2009-06-01
Printed: Jun 2009
Printed: Jun 2009
- Indranil Biswas
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] |