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ISSN 1088-6850(e) ISSN 0002-9947(p)

Splitting of gauge groups

Author(s): Daisuke Kishimoto; Akira Kono
Journal: Trans. Amer. Math. Soc. 362 (2010), 6715-6731.
MSC (2000): Primary 57S05, 55R70; Secondary 54C35
Posted: August 3, 2010
MathSciNet review: 2678992
Retrieve article in: PDF

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Abstract: Let be a topological group and let be a principal -bundle over a based space . We denote the gauge group of by $\mathcal{G}(P)$ and the based gauge group of by $\mathcal{G}_0(P)$ . Then the inclusion of the basepoint of induces the exact sequence of topological groups $1\to\mathcal{G}_0(P)\to\mathcal{G}(P)\to G\to 1$ . We study the splitting of this exact sequence in the category of -spaces and -maps in connection with the triviality of the adjoint bundle of and with the higher homotopy commutativity of .

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