Scharlemann ’ s manifold is standard

  title={Scharlemann ’ s manifold is standard},
  author={Selman Akbulut},
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 × S1, along a loop in Σ × 1 ⊂ Σ × S1 normally generating the fundamental group of Σ, one obtains a closed smooth manifold… CONTINUE READING