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A note on the homotopy type of certain gauge groups. (English) Zbl 0722.55008
Summary: Let \(G_ k\) be the gauge group of \(P_ k\), the principal SU(2) bundle over \(S^ 4\) with \(c_ 2(P_ k)=k\). In this paper we show that \(G_ k\simeq G_{k'}\) if and only if \((12,k)=(12,k')\) where (12,k) is te GCD of 12 and k.

MSC:
55R15 Classification of fiber spaces or bundles in algebraic topology
55P15 Classification of homotopy type
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References:
[1] Atiyah, Philos. Trans. Roy. Soc. London Ser. A 308 pp 523– (1982) · Zbl 0509.14014
[2] DOI: 10.1090/S0002-9947-1972-0309111-X
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