A note on the homotopy type of certain gauge groups

Abstract

Synopsis 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 ≃ G k . if and only if (12, k ) = (12, k ′) where (12, k ) is the GCD of 12 and k .