SCHARLEMANN’S MANIFOLD IS STANDARD

SELMAN AKBULUT

Abstract. In his 1974 thesis, Martin Scharlemann constructed a fake homotopy equivalence from a closed smooth manifold f : Q → S^{3} × S^{1} # S^{2} × S^{2}, and asked whether the manifold Q itself is diffeomorphic to S^{3}×S^{1} # S^{2}×S^{2}. Here we answer this question affirmatively.