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Peer-reviewedCC BYGeometry & Topology

Corks for exotic diffeomorphisms

  • Vyacheslav Krushkal1
  • Anubhav Mukherjee2
  • Mark Powell3
  • Terrin Warren4
4 affiliations
  1. 1Department of Mathematics, University of Virginia, Charlottesville, VA, United States
  2. 2Department of Mathematics, Princeton University, Princeton, NJ, United States
  3. 3School of Mathematics and Statistics, University of Glasgow, Glasgow, United Kingdom
  4. 4Department of Mathematics, California Polytechnic State University, San Luis Obispo, CA, United States
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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 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 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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Cite

BibTeXRIS
BibTeX
@article{krushkal2026corks,
  title = {{Corks for exotic diffeomorphisms}},
  author = {Vyacheslav Krushkal and Anubhav Mukherjee and Mark Powell and Terrin Warren},
  journal = {Geometry \& Topology},
  year = {2026},
  month = jul,
  doi = {10.2140/gt.2026.30.2297},
  url = {https://doi.org/10.2140/gt.2026.30.2297},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Corks for exotic diffeomorphisms
AU  - Vyacheslav Krushkal
AU  - Anubhav Mukherjee
AU  - Mark Powell
AU  - Terrin Warren
PY  - 2026
DA  - 2026/07/31
JO  - Geometry & Topology
DO  - 10.2140/gt.2026.30.2297
UR  - https://doi.org/10.2140/gt.2026.30.2297
AB  - 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 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 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.
SN  - 1364-0380
SN  - 1465-3060
ER  -