Théorie de jauge et symétries des fibrés

Brandt, D.; Hausmann, Jean-Claude

doi:10.5802/aif.1344

Brandt, D. ; Hausmann, Jean-Claude

Annales de l'Institut Fourier, Tome 43 (1993) no. 2, pp. 509-537.

Résumé
Abstract

Soit $ξ$ 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 $Γ$ sur $M$ , on se pose la question de savoir si elle provient d’une action sur le fibré $ξ$ . L’originalité de ce travail est de relier ce problème à l’existence de points fixes pour les actions de $Γ$ que l’on induit naturellement sur divers espaces de modules de $G$ -connexions sur $ξ$ .

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 $M$ .

MR Zbl

DOI : 10.5802/aif.1344

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     author = {Brandt, D. and Hausmann, Jean-Claude},
     title = {Th\'eorie de jauge et sym\'etries des fibr\'es},
     journal = {Annales de l'Institut Fourier},
     pages = {509--537},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {43},
     number = {2},
     year = {1993},
     doi = {10.5802/aif.1344},
     mrnumber = {94c:57056},
     zbl = {0778.57018},
     language = {fr},
     url = {https://www.numdam.org/articles/10.5802/aif.1344/}
}

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Brandt, D.; Hausmann, Jean-Claude. Théorie de jauge et symétries des fibrés. Annales de l'Institut Fourier, Tome 43 (1993) no. 2, pp. 509-537. doi : 10.5802/aif.1344. https://www.numdam.org/articles/10.5802/aif.1344/

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Guijarro, Luis; Sadun, Lorenzo; Walschap, Gerard Parallel connections over symmetric spaces, The Journal of Geometric Analysis, Volume 11 (2001) no. 2, p. 265 | DOI:10.1007/bf02921966

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