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We prove a localization theorem for exotic diffeomorphisms, showing that every diffeomorphism of a compact simply-connected 4-manifold that is isotopic to the identity after stabilizing with one copy of S² S², is smoothly isotopic to a diffeomorphism that is supported on a contractible submanifold. For those that require more than one copy of S² S², we prove that the diffeomorphism can be isotoped to one that is supported in a submanifold homotopy equivalent to a wedge of 2-spheres, with null-homotopic inclusion map. We investigate the implications of these results by applying them to known exotic diffeomorphisms.
Krushkal et al. (Fri,) studied this question.
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