Diffeomorphisms of 4-manifolds with boundary and exotic embeddings

TL;DR

This paper introduces family invariants for 4-manifolds with contact boundary to detect exotic diffeomorphisms and presents the first example of exotic 3-spheres within a smooth closed 4-manifold, revealing new phenomena in 4-dimensional topology.

Contribution

It develops family versions of Kronheimer and Mrowka's invariant and demonstrates the existence of exotic 3-spheres in 4-manifolds, advancing understanding of smooth structures.

Findings

Family invariants detect exotic diffeomorphisms

Existence of exotic 3-spheres in 4-manifolds

New phenomena in 4-dimensional topology

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.