Théorie de jauge et symétries des fibrés

D. Brandt; Jean-Claude Hausmann

Annales de l'institut Fourier (1993)

  • Volume: 43, Issue: 2, page 509-537
  • ISSN: 0373-0956

Abstract

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Let ξ be a smooth G -principal bundle over a manifold M ( G being a compact Lie group). Given an action of a compact Lie group Γ on M , one asks the question whether it comes from an action on the bundle ξ . In this paper, this question is shown to be essentially equivalent to the existence of fixed points for the naturally induced actions of Γ on various moduli spaces of G -connections on M .

How to cite

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Brandt, D., and Hausmann, Jean-Claude. "Théorie de jauge et symétries des fibrés." Annales de l'institut Fourier 43.2 (1993): 509-537. <http://eudml.org/doc/75008>.

@article{Brandt1993,
abstract = {Soit $\xi $ un $G$-fibré principal différentiable sur une variété $M$ ($G$ un groupe de Lie compact). Étant donné une action d’un groupe de Lie compact $\Gamma $ sur $M$, on se pose la question de savoir si elle provient d’une action sur le fibré $\xi $. L’originalité de ce travail est de relier ce problème à l’existence de points fixes pour les actions de $\Gamma $ que l’on induit naturellement sur divers espaces de modules de $G$-connexions sur $\xi $.},
author = {Brandt, D., Hausmann, Jean-Claude},
journal = {Annales de l'institut Fourier},
keywords = {principal bundles; lifting actions of compact groups; gauge group; fixed point; spaces of connections},
language = {fre},
number = {2},
pages = {509-537},
publisher = {Association des Annales de l'Institut Fourier},
title = {Théorie de jauge et symétries des fibrés},
url = {http://eudml.org/doc/75008},
volume = {43},
year = {1993},
}

TY - JOUR
AU - Brandt, D.
AU - Hausmann, Jean-Claude
TI - Théorie de jauge et symétries des fibrés
JO - Annales de l'institut Fourier
PY - 1993
PB - Association des Annales de l'Institut Fourier
VL - 43
IS - 2
SP - 509
EP - 537
AB - Soit $\xi $ un $G$-fibré principal différentiable sur une variété $M$ ($G$ un groupe de Lie compact). Étant donné une action d’un groupe de Lie compact $\Gamma $ sur $M$, on se pose la question de savoir si elle provient d’une action sur le fibré $\xi $. L’originalité de ce travail est de relier ce problème à l’existence de points fixes pour les actions de $\Gamma $ que l’on induit naturellement sur divers espaces de modules de $G$-connexions sur $\xi $.
LA - fre
KW - principal bundles; lifting actions of compact groups; gauge group; fixed point; spaces of connections
UR - http://eudml.org/doc/75008
ER -

References

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  6. [LMS] R. LASHOF & J. MAY & G. SEGAL, Equivariant bundles with abelian structural group, Contemporary Math., Vol 19 (AMS 1983), 167-176. Zbl0526.55020MR85b:55023
  7. [KN] S. KOBAYASHI & K. NOMIZU, Foundations of differential topology, Vol I et II, Interscience, New York, 1969. Zbl0175.48504
  8. [PS] R. PALAIS & T. STUART, The cohomology of differentiable transformation groups, Amer. J. of Math., 83 (1961), 623-644. Zbl0104.17703MR25 #4030
  9. [St] T. STUART, Lifting group actions in fibre bundle, Annals of Math., 74 (1961), 192-198. Zbl0116.40502MR23 #A3798
  10. [VE] van EST, On the algebraic cohomology concepts in Lie groups, Indigat. Math., 18 (1955), I, 225-233 ; II, 286-294. Zbl0067.26202MR17,61b
  11. [Wa] Sh. WANG, Moduli spaces over manifolds with involutions, to appear (Preprint, Michigan State Univ. at East Lansing). 

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