Cosmetic operations and Khovanov multicurves
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866910510301052928 |
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| author | Kotelskiy, Artem Lidman, Tye Moore, Allison H. Watson, Liam Zibrowius, Claudius |
| author_facet | Kotelskiy, Artem Lidman, Tye Moore, Allison H. Watson, Liam Zibrowius, Claudius |
| contents | We prove an equivariant version of the Cosmetic Surgery Conjecture for strongly invertible knots. Our proof combines a recent result of Hanselman with the Khovanov multicurve invariants $\widetilde{\operatorname{Kh}}$ and $\widetilde{\operatorname{BN}}$. We apply the same techniques to reprove a result of Wang about the Cosmetic Crossing Conjecture and split links. Along the way, we show that $\widetilde{\operatorname{Kh}}$ and $\widetilde{\operatorname{BN}}$ detect if a Conway tangle is split. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_14049 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Cosmetic operations and Khovanov multicurves Kotelskiy, Artem Lidman, Tye Moore, Allison H. Watson, Liam Zibrowius, Claudius Geometric Topology Quantum Algebra Symplectic Geometry We prove an equivariant version of the Cosmetic Surgery Conjecture for strongly invertible knots. Our proof combines a recent result of Hanselman with the Khovanov multicurve invariants $\widetilde{\operatorname{Kh}}$ and $\widetilde{\operatorname{BN}}$. We apply the same techniques to reprove a result of Wang about the Cosmetic Crossing Conjecture and split links. Along the way, we show that $\widetilde{\operatorname{Kh}}$ and $\widetilde{\operatorname{BN}}$ detect if a Conway tangle is split. |
| title | Cosmetic operations and Khovanov multicurves |
| topic | Geometric Topology Quantum Algebra Symplectic Geometry |
| url | https://arxiv.org/abs/2109.14049 |