Splitting of gauge groups

Kishimoto, Daisuke; Kono, Akira

doi:10.1090/S0002-9947-2010-05207-9

Splitting of gauge groups
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by Daisuke Kishimoto and Akira Kono PDF

Trans. Amer. Math. Soc. 362 (2010), 6715-6731 Request permission

Abstract:

Let $G$ be a topological group and let $P$ be a principal $G$-bundle over a based space $B$. We denote the gauge group of $P$ by $\mathcal {G}(P)$ and the based gauge group of $P$ by $\mathcal {G}_0(P)$. Then the inclusion of the basepoint of $B$ 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 $A_n$-spaces and $A_n$-maps in connection with the triviality of the adjoint bundle of $P$ and with the higher homotopy commutativity of $G$.

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