Gompf's cork and Heegaard Floer homology
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912009520414720 |
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| author | Dai, Irving Mallick, Abhishek Zemke, Ian |
| author_facet | Dai, Irving Mallick, Abhishek Zemke, Ian |
| contents | Gompf showed that for $K$ in a certain family of double-twist knots, the swallow-follow operation makes $1/n$-surgery on $K \# -K$ into a cork boundary. We derive a general Floer-theoretic condition on $K$ under which this is the case. Our formalism allows us to produce many further examples of corks, partially answering a question of Gompf. Unlike Gompf's method, our proof does not rely on any closed 4-manifold invariants or effective embeddings, and also generalizes to other diffeomorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08258 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Gompf's cork and Heegaard Floer homology Dai, Irving Mallick, Abhishek Zemke, Ian Geometric Topology 57R58, 57R55 Gompf showed that for $K$ in a certain family of double-twist knots, the swallow-follow operation makes $1/n$-surgery on $K \# -K$ into a cork boundary. We derive a general Floer-theoretic condition on $K$ under which this is the case. Our formalism allows us to produce many further examples of corks, partially answering a question of Gompf. Unlike Gompf's method, our proof does not rely on any closed 4-manifold invariants or effective embeddings, and also generalizes to other diffeomorphisms. |
| title | Gompf's cork and Heegaard Floer homology |
| topic | Geometric Topology 57R58, 57R55 |
| url | https://arxiv.org/abs/2312.08258 |