Irreducible 4-manifolds can admit exotic diffeomorphisms

TL;DR

This paper demonstrates that certain irreducible 4-manifolds, specifically minimal complex surfaces, can admit exotic diffeomorphisms, expanding understanding of smooth structures in four-dimensional topology.

Contribution

It provides the first known examples of exotic diffeomorphisms on irreducible 4-manifolds and establishes conditions for non-trivial boundary Dehn twists in spin 4-manifolds.

Findings

Existence of exotic diffeomorphisms on minimal complex surfaces.

Sufficient conditions for non-trivial boundary Dehn twists.

New examples of non-trivial boundary Dehn twists.

Abstract

We prove that a variety of examples of minimal complex surfaces admit exotic diffeomorphisms, providing the first known instances of exotic diffeomorphisms of irreducible 4-manifolds. We also give sufficient conditions for the boundary Dehn twist on a spin 4-manifold with $S^3$ boundary to be non-trivial in the relative mapping class group. This gives many new examples of non-trivial boundary Dehn twists.