Representing homology classes of simply connected 4-manifolds

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 S-2 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 S-4, then each element of H-2 (W; Z) can be represented by a locally flat topological embedding of S-2. (C) 2002 Elsevier Science B.V. All rights reserved.