Irreducible 4-manifolds can admit exotic diffeomorphisms

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.