Abstract
There is widespread interest in the gauge groups of principal SU(n)-bundles over simply-connected four-manifolds, and the gauge groups of principal U(n)-bundles over compact, orientable surfaces. We show that in the stable case of SU(∞) (resp. U(∞)), the gauge groups decompose, up to a multiplicative homotopy which holds integrally, as an explicit product where each factor is an iterated loop space of SU(∞) (resp. U(∞)).
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References
Atiyah M.F., Bott R.: The Yang-Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser. A 308, 523–615 (1983)
Bradlow S.B., Garcia-Prada O., Gothen P.B.: Homotopy groups of moduli spaces of representations. Topology 47, 203–224 (2008)
Daskalopoulos G.D., Uhlenbeck K.K.: An application of transversality to the topology of the moduli space of stable bundles. Topology 34, 203–215 (1995)
Kishimoto D., Kono A.: Splitting of gauge groups, Trans. Amer. Math. Soc. 362, 6715–6731 (2010)
Kishimoto D., Kono A., Theriault S.: Homotopy commutativity in p-localized gauge groups, Proc. Roy. Soc. Edin. 143, 851–870 (2013)
D. Kishimoto, A. Kono and S. Theriault, Refined decompositions of gauge groups, to appear in Kyoto J. Math.
Kishimoto D., Kono A., Tsutaya M.: Mod-p decompositions of gauge groups, Algebr. Geom. Topol. 13, 1757–1778 (2013)
Theriault S.D.: Odd primary homotopy decompositions of gauge groups, Algebr. Geom. Topol. 10, 535–564 (2010)
Theriault S.D.: Homotopy decompositions of gauge groups over Riemann surfaces and applications to moduli spaces, Int. J. Math. 22, 1711–1719 (2011)
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Theriault, S. Homotopy decompositions of stable gauge groups. Arch. Math. 103, 493–498 (2014). https://doi.org/10.1007/s00013-014-0708-3
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DOI: https://doi.org/10.1007/s00013-014-0708-3