Homotopy types of SU(n)-gauge groups over non-spin 4-manifolds

Abstract

Let M be an orientable, simply-connected, closed, non-spin 4-manifold and let G k (M) be the gauge group of the principal G-bundle over M with second Chern class k ∈ Z. It is known that the homotopy type of G k (M) is determined by the homotopy type of G k (CP 2 ). In this paper we investigate properties of G k (CP 2 ) when G = SU (n) that partly classify the homotopy types of the gauge groups.