Topology and its Applications
The main theorem asserts that every 2-dimensional homology class of a compact simply connected PL 4-manifold can be represented by a codimension-0 submanifold consisting of a contractible manifold with a single 2-handle attached. One consequence of the theorem is the fact that every map of S2 into a simply connected, compact PL 4-manifold is homotopic to an embedding if and only if the same is true for every homotopy equivalence. The theorem is also the main ingredient in the proof of the following result: If W is a compact, simply connected, PL submanifold of S4, then each element of H2(W;ℤ) can be represented by a locally flat topological embedding of S2.
Liem, Vo Thanh and Venema, Gerard A., "Representing homology classes of simply connected 4-manifolds" (2002). University Faculty Publications and Creative Works. 509.