Pseudo‐isotopies and diffeomorphisms of 4‐manifolds

Abstract A diffeomorphism of a compact manifold is pseudo‐isotopic to the identity if there is a diffeomorphism of which restricts to on , and which restricts to the identity on and . We construct examples of diffeomorphisms of 4‐manifolds which are pseudo‐isotopic but not isotopic to the identity. To do so, we further understanding of which elements of the ‘second pseudo‐isotopy obstruction’, defined by Hatcher and Wagoner, can be realised by pseudo‐isotopies of 4‐manifolds. We also prove that all elements of the first and second pseudo‐isotopy obstructions can be realised after connected sums with copies of .