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Let $M$ be an orientable, simply-connected, closed, non-spin 4-manifold andlet $\mathcal{G}_k(M)$ be the gauge group of the principal $G$-bundle over $M$with second Chern class $k\in\mathbb{Z}$. It is known that the homotopy type of$\mathcal{G}_k(M)$ is determined by the homotopy type of$\mathcal{G}_k(\mathbb{CP}^2)$. In this paper we investigate properties of$\mathcal{G}_k(\mathbb{CP}^2)$ when $G = SU(n)$ that partly classify thehomotopy types of the gauge groups.

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