Equivariant principal bundles for G–actions and G–connections

Indranil Biswas; S. Senthamarai Kannan; D. S. Nagaraj

Complex Manifolds (2015)

  • Volume: 2, Issue: 1, page 178-185, electronic only
  • ISSN: 2300-7443

Abstract

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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.

How to cite

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Indranil Biswas, S. Senthamarai Kannan, and D. S. Nagaraj. "Equivariant principal bundles for G–actions and G–connections." Complex Manifolds 2.1 (2015): 178-185, electronic only. <http://eudml.org/doc/275980>.

@article{IndranilBiswas2015,
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.},
author = {Indranil Biswas, S. Senthamarai Kannan, D. S. Nagaraj},
journal = {Complex Manifolds},
keywords = {Equivariant bundles; G–connection; flatness; toric variety; equivariant bundles; -connection},
language = {eng},
number = {1},
pages = {178-185, electronic only},
title = {Equivariant principal bundles for G–actions and G–connections},
url = {http://eudml.org/doc/275980},
volume = {2},
year = {2015},
}

TY - JOUR
AU - Indranil Biswas
AU - S. Senthamarai Kannan
AU - D. S. Nagaraj
TI - Equivariant principal bundles for G–actions and G–connections
JO - Complex Manifolds
PY - 2015
VL - 2
IS - 1
SP - 178
EP - 185, electronic only
AB - 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.
LA - eng
KW - Equivariant bundles; G–connection; flatness; toric variety; equivariant bundles; -connection
UR - http://eudml.org/doc/275980
ER -

References

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  1. [1] M. F. Atiyah, Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc. 85 (1957), 181–207. Zbl0078.16002
  2. [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. Zbl06537053
  3. [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. 
  4. [4] I. Moerdijk and J. Mrˇcun, Introduction to foliations and Lie groupoids, Cambridge Studies in Advanced Mathematics, 91, Cambridge University Press, Cambridge, 2003. 

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