An obstruction to smooth isotopy in dimension 4

Abstract

Techniques of gauge theory are used to define and compute an invariant of certain diffeomorphisms of 4-manifolds. The invariant vanishes for any diffeomorphism which is smoothly isotopic to the identity. As an application, we give the first example of a diffeomorphism of a simply-connected 4-manifold which is homotopic to the identity map, but not smoothly isotopic to the identity.

Minor revisions (typos and one formula). AMS-LaTeX. 17 pages, 2 postscript figures. To appear in Mathematical Research Letters

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