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 {mathcal {G}}_k(M) be the gauge group of the principal G-bundle over M with second Chern class kin {mathbb {Z}}. It is known that the homotopy type of {mathcal {G}}_k(M) is determined by the homotopy type of {mathcal {G}}_k({mathbb {C}}{mathbb {P}}^2). In this paper we investigate properties of {mathcal {G}}_k({mathbb {C}}{mathbb {P}}^2) when G=SU(n) that partly classify the homotopy types of the gauge groups.