Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

A note on the homotopy type of certain gauge groups

Akira Konoa1

a1 Department of Mathematics, Kyoto University, Kyoto 606, Japan and Department of Mathematical Sciences, University of Aberdeen, The Edward Wright Building, Dunbar Street, Aberdeen AB9 2TY, U.K.


Let Gk be the gauge group of Pk, the principal SU(2) bundle over S4 with c2(Pk) = k. In this paper we show that GkGk. if and only if (12, k) = (12, k′) where (12, k) is the GCD of 12 and k.

(Received March 20 1990)

(Revised July 06 1990)