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 $k\in\mathbb{ Z}$. 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 the homotopy types of the gauge groups.
Categories: math.AT