2-cabling and tangle operators in Khovanov theory
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918110109368320 |
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| author | Marian, Mihai |
| author_facet | Marian, Mihai |
| contents | We describe an operator on 4-ended tangles that is induced by 2-cabling of a strongly invertible knot. By passing to the 4-ended tangle Khovanov theory of Kotelskiy-Watson-Zibrowius, this induces an operator on the category of type D structures over the Bar-Natan algebra $\mathcal{B}$, as well as on a Fukaya category of the 4-punctured 2-sphere. We provide a full description of this operator's restriction to cap-trivial tangles. Finally, we extract geography results that are inspired by a recent concordance invariant of Lewark-Zibrowius. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00644 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | 2-cabling and tangle operators in Khovanov theory Marian, Mihai Geometric Topology We describe an operator on 4-ended tangles that is induced by 2-cabling of a strongly invertible knot. By passing to the 4-ended tangle Khovanov theory of Kotelskiy-Watson-Zibrowius, this induces an operator on the category of type D structures over the Bar-Natan algebra $\mathcal{B}$, as well as on a Fukaya category of the 4-punctured 2-sphere. We provide a full description of this operator's restriction to cap-trivial tangles. Finally, we extract geography results that are inspired by a recent concordance invariant of Lewark-Zibrowius. |
| title | 2-cabling and tangle operators in Khovanov theory |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2508.00644 |