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Connections on a Parabolic Principal Bundle, II

Published online by Cambridge University Press:  20 November 2018

Indranil Biswas
Indranil Biswas*
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India e-mail: indranil@math.tifr.res.in
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Abstract

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In 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

32L0514F05Parabolic bundleAtiyah exact sequenceconnection
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 2 , 01 June 2009 , pp. 175 - 185
Copyright
Copyright © Canadian Mathematical Society 2009

References

[At] Atiyah, M. F., Complex analytic connections in fibre bundles. Trans. Amer. Math. Soc. 85(1957), 181–207.Google Scholar
[BBN1] Balaji, V., Biswas, I., and Nagaraj, D. S., Principal bundles over projective manifolds with parabolic structure over a divisor. Tohoku Math. J. 53(2001), no. 3, 337–367.Google Scholar
[BBN2] Balaji, V., Biswas, I., and Nagaraj, D. S., Ramified G-bundles as parabolic bundles. J. Ramanujan Math. Soc. 18(2003), no. 2, 123–138.Google Scholar
[Bi1] Biswas, I., Parabolic bundles as orbifold bundles. Duke Math. J. 88(1997), no. 2, 305–325.Google Scholar
[Bi2] Biswas, I., Connections on a parabolic principal bundle over a curve. Canad. J. Math. 58(2006), no. 2, 262–281.Google Scholar
[No1] Nori, M. V., On the representations of the fundamental group. Compositio Math. 33(1976), no. 1, 29–41.Google Scholar
[No2] Nori, M. V., The fundamental group-scheme. Proc. Indian Acad. Sci. Math. Sci. 91(1982), no. 2, 73–122.Google Scholar