In his 1974 thesis, Martin Scharlemann constructed a fake homotopy equivalence from a closed smooth manifold f : Q → S3 × S1#S2 × S2, and asked the question whether or not the manifold Q itself is diffeomorphic to S3 × S1#S2 × S2. Here we answer this question affirmatively. In [Sc] Scharlemann showed that if Σ3 is the Poincaré homology 3-sphere, by surgering the 4-manifold Σ× S, along a loop in...
