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Note on mod \(p\) decompositions of gauge groups. (English) Zbl 1190.55007
Summary: We give fibrewise mod \(p\) decompositions of the adjoint bundle of a principal \(G\)-bundle \(P\) when the topological group \(G\) has mod \(p\) decompositions by automorphisms as in [B. Harris, Ann. Math. (2) 74, 407–413 (1961; Zbl 0118.18501)], which imply mod \(p\) decompositions of the gauge group of \(P\).

MSC:
55R70 Fibrewise topology
57S05 Topological properties of groups of homeomorphisms or diffeomorphisms
55R10 Fiber bundles in algebraic topology
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[1] M. F. Atiyah and R. Bott, The Yangmhy Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser. A 308 (1983), no. 1505, 523-615. · Zbl 0509.14014
[2] A. Borel and J.-P. Serre, Groupes de Lie et puissances rĂ©duites de Steenrod, Amer. J. Math. 75 (1953), 409-448. · Zbl 0050.39603
[3] M. Crabb and I. James, Fibrewise homotopy theory , Springer, London, 1998. · Zbl 0905.55001
[4] J. A. Wolf and A. Gray, Homogeneous spaces defined by Lie group automorphisms. I, J. Differential Geometry 2 (1968), 77-114. · Zbl 0169.24103
[5] B. Harris, On the homotopy groups of the classical groups, Ann. of Math. (2) 74 (1961), 407-413. · Zbl 0118.18501
[6] P. Hilton, G. Mislin and J. Roitberg, Localization of nilpotent groups and spaces , North-Holland, Amsterdam, 1975. · Zbl 0323.55016
[7] D. Kishimoto and A. Kono, Splitting of gauge groups, Trans. Amer. Math. Soc. (to appear). · Zbl 1210.57034
[8] A. Kono and S. Tsukuda, Note on the triviality of adjoint bundles, Contemp. Math. (to appear). · Zbl 1209.55004
[9] J. P. May, Fibrewise localization and completion , Trans. Amer. Math. Soc. 258 (1980), no. 1, 127-146. · Zbl 0429.55004
[10] J. M. M\oller, Nilpotent spaces of sections , Trans. Amer. Math. Soc. 303 (1987), no. 2, 733-741. · Zbl 0628.55007
[11] S.D. Theriault, Odd primary homotopy decompositions of gauge groups. (Preprint). · Zbl 1196.55009
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