Abstract
In his 1974 thesis, Martin Scharlemann constructed a fake homotopy equivalence from a closed smooth manifold $f\colon Q \to S^3 \times S^1\#S^2 \times S^2$, and asked the question whether or not the manifold $Q$ itself is diffeomorphic to $S^3 \times S^1\#S^2 \times S^2$. Here we answer this question affirmatively.
