Modpdecompositions of gauge groups

Abstract

We give mod p decompositions of homotopy types of the gauge groups of principal bundles over spheres, which are compatible with mod p decompositions of Lie groups given by Mimura, Nishida and Toda. As an application, we also give some computations on the homotopy types of gauge groups. In particular, we show the p–local converse of the result of Sutherland on the classifications of the gauge groups of principal SU.n/–bundles.