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Corks for exotic
diffeomorphisms
Vyacheslav Krushkal, Anubhav Mukherjee, Mark Powell and Terrin Warren |
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Geometry & Topology 30 (2026) 2297–2335
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Abstract |
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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 is smoothly isotopic to a diffeomorphism that is supported on a contractible submanifold. For those that require more than one copy of , 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. |
Keywords
$4$-manifolds, diffeomorphisms, corks
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Mathematical Subject Classification
Primary: 57K40, 57N37, 57R58
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References |
Publication
Received: 10 September 2024
Revised: 27 January 2026
Accepted: 25 February 2026
Published: 31 July 2026
Proposed: Ciprian Manolescu
Seconded: Benson Farb, Ian Agol
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Authors |
| Vyacheslav Krushkal | |
| Department of Mathematics University of Virginia Charlottesville, VA United States |
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| Anubhav Mukherjee | |
| Department of Mathematics Princeton University Princeton, NJ United States |
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| Mark Powell | |
| School of Mathematics and
Statistics University of Glasgow Glasgow United Kingdom |
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| Terrin Warren | |
| Department of Mathematics California Polytechnic State University San Luis Obispo, CA United States |
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| © 2026 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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