  It is one of the most important facts in 4-dimensional topology that not
every spherical homology class of a 4-manifold can be represented by an
embedded sphere. In 1978, M. Freedman and R. Kirby showed that in the simply
connected case, many of the obstructions to constructing such a sphere vanish
if one modifies the ambient 4-manifold by adding products of 2-spheres, a
process which is usually called stabilisation. In this paper, we extend this
result to non-simply connected 4-manifolds and show how it is related to the
Spin^c-bordism groups of Eilenberg-MacLane spaces.
