Corks for exotic diffeomorphisms
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911470833369088 |
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| author | Krushkal, Vyacheslav Mukherjee, Anubhav Powell, Mark Warren, Terrin |
| author_facet | Krushkal, Vyacheslav Mukherjee, Anubhav Powell, Mark Warren, Terrin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04696 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Corks for exotic diffeomorphisms Krushkal, Vyacheslav Mukherjee, Anubhav Powell, Mark Warren, Terrin Geometric Topology 57K40, 57N37, 57R58 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. |
| title | Corks for exotic diffeomorphisms |
| topic | Geometric Topology 57K40, 57N37, 57R58 |
| url | https://arxiv.org/abs/2407.04696 |