Unstable <i>K</i>¹-group and homotopy type of certain gauge groups

Abstract

We denote the group of homotopy set [ X, U ( n )] by the unstable K 1 -group of X . In this paper, using the unstable K 1 -group of the multi-suspended CP 2 , we give a necessary condition for two principal SU( n )-bundles over § 4 to have the associated gauge group of the same homotopy type, which is an improvement of the result of Sutherland and, particularly, show the complete classification of homotopy types of SU(3)-gauge groups over S 4 .