The suspension of a 4-manifold and its applications

Abstract

Let $M$ be a smooth, orientable, closed, connected $4$-manifold and suppose that $H_1(M;\mathbb{Z})$ is finitely generated and has no $2$-torsion. We give a homotopy decomposition of the suspension of $M$ in terms of spheres, Moore spaces and $\Sigma \mathbb{C}{P}^2$. This is used to calculate any reduced generalized cohomology theory of $M$ as a group and to determine the homotopy types of certain current groups and gauge groups.

arXiv comment26 pages; accepted by Israel Journal of Mathematics