Talk:Integral homology 3-spheres embed (Ex)

Take Freedman’s contractible 4-manifold bounding the given homology sphere and double it. The result is a simply-connected closed 4-manifold with trivial 2nd homology (since compact (?) manifolds with boundary admit collars also in the topological category we are able to apply the Seifert-van Kampen and Mayer-Vietoris theorems) thus homeomorphic to $S^4$. Fusing the two collars gives the tubular neighbourhood around the embedded 3-manifold.