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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
Keywords:
gauge group; principal SU(2) bundle
Full Text:
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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