Corks for exotic diffeomorphisms

Vyacheslav Krushkal; Anubhav Mukherjee; Mark Powell; Terrin Warren

doi:10.2140/gt.2026.30.2297

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arXiv · 2407.04696

Corks for exotic diffeomorphisms

Vyacheslav Krushkal·Anubhav Mukherjee·Mark Powell·Terrin Warren

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Abstract

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 $S^2 \times S^2$, is smoothly isotopic to a diffeomorphism that is supported on a contractible submanifold. For those that require more than one copy of $S^2 \times S^2$, 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.

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BibTeX RIS

Vyacheslav Krushkal, Anubhav Mukherjee, Mark Powell, Terrin Warren. 2024-07-05. Corks for exotic diffeomorphisms. https://doi.org/10.2140/gt.2026.30.2297

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