In general, homology groups rarely determine the homotopy type of spaces. It is therefore of interest to find special cases when this happens. Let M be a smooth, orientable, closed, connected 4-manifold such that its first homology group has no 2-torsion. We give a homotopy decomposition of the suspension of M in terms of spheres, Moore spaces and the suspended CP^2. This is used to calculate the K-theory of M as a group and to determine the homotopy type of certain current groups and gauge groups.

This is joint work with Stephen Theriault.