Smoothing 3-manifolds in 5-manifolds

Abstract

We show that every locally flat topological embedding of a 3-manifold in a smooth 5-manifold is homotopic, by a small homotopy, to a smooth embedding. We deduce that topologically locally flat concordance implies smooth concordance for smooth surfaces in smooth 4-manifolds.

15 pages, 3 figures. v2: referee's comments incorporated. To appear in Inventiones Mathematicae