Mod $p$ decompositions 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 $SU\left(n\right)$–bundles.