Functoriality of Odd and Generalized Khovanov Homology in $\mathbb{R}^3\times I$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913684397228032 |
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| author | Migdail, Jacob Wehrli, Stephan |
| author_facet | Migdail, Jacob Wehrli, Stephan |
| contents | We extend the generalized Khovanov bracket to smooth link cobordisms in $\mathbb{R}^3\times I$ and prove that the resulting theory is functorial up to global invertible scalars. The generalized Khovanov bracket can be specialized to both even and odd Khovanov homology. Particularly by setting $π=-1$, we obtain that odd Khovanov homology is functorial up to sign. We end by showing that odd Khovanov homology is not functorial under smooth link cobordisms in $S^3\times I$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_23455 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Functoriality of Odd and Generalized Khovanov Homology in $\mathbb{R}^3\times I$ Migdail, Jacob Wehrli, Stephan Geometric Topology 57K18 We extend the generalized Khovanov bracket to smooth link cobordisms in $\mathbb{R}^3\times I$ and prove that the resulting theory is functorial up to global invertible scalars. The generalized Khovanov bracket can be specialized to both even and odd Khovanov homology. Particularly by setting $π=-1$, we obtain that odd Khovanov homology is functorial up to sign. We end by showing that odd Khovanov homology is not functorial under smooth link cobordisms in $S^3\times I$. |
| title | Functoriality of Odd and Generalized Khovanov Homology in $\mathbb{R}^3\times I$ |
| topic | Geometric Topology 57K18 |
| url | https://arxiv.org/abs/2410.23455 |