Diffeomorphisms of 4-manifolds with boundary and exotic embeddings

Abstract

We define family versions of the invariant of 4-manifolds with contact boundary due to Kronheimer and Mrowka and use these to detect exotic diffeomorphisms of 4-manifolds with boundary. Further, we show the existence of the first example of exotic 3-spheres in a smooth closed 4-manifold with diffeomorphic complements.

45 pages, 2 figures, several parts (including Introduction) have been changed. To appear in Math. Ann