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Complex Manifolds

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2300-7443
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Equivariant principal bundles for G–actions and G–connections

Indranil Biswas
  • Corresponding author
  • School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ S. Senthamarai Kannan
  • Corresponding author
  • Chennai Mathematical Institute, H1, SIPCOT IT Park, Siruseri, Kelambakkam 603103, India
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ D. S. Nagaraj
  • Corresponding author
  • The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
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  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-12-21 | DOI: https://doi.org/10.1515/coma-2015-0013

Abstract

Given a complex manifold M equipped with an action of a group G, and a holomorphic principal H–bundle EH on M, we introduce the notion of a connection on EH along the action of G, which is called a G–connection. We show some relationship between the condition that EH admits a G–equivariant structure and the condition that EH admits a (flat) G–connection. The cases of bundles on homogeneous spaces and smooth toric varieties are discussed.

Keywords: Equivariant bundles; G–connection; flatness; toric variety

References

  • [1] M. F. Atiyah, Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc. 85 (1957), 181–207. Google Scholar

  • [2] I Biswas, A. Dey and M. Poddar, Equivariant principal bundles and logarithmic connections on toric varieties, Pacific Jour. Math. (to appear), arXiv:1507.02415. Google Scholar

  • [3] N. Bourbaki, ´El´ements demath´ematique. XXVI. Groupes et alg`ebres de Lie. Chapitre 1: Alg`eebres de Lie, Actualit´es Sci. Ind. No. 1285, Hermann, Paris 1960. Google Scholar

  • [4] I. Moerdijk and J. Mrˇcun, Introduction to foliations and Lie groupoids, Cambridge Studies in Advanced Mathematics, 91, Cambridge University Press, Cambridge, 2003. Google Scholar

About the article

Received: 2015-07-18

Accepted: 2015-12-18

Published Online: 2015-12-21


Citation Information: Complex Manifolds, Volume 2, Issue 1, ISSN (Online) 2300-7443, DOI: https://doi.org/10.1515/coma-2015-0013.

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© 2015 I. Biswas et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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