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arXiv · 2410.23455

Functoriality of Odd and Generalized Khovanov Homology in $\mathbb{R}^3\times I$

Jacob Migdail·Stephan Wehrli
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Abstract

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 $S^3\times I$.

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Jacob Migdail, Stephan Wehrli. 2025-02-08. Functoriality of Odd and Generalized Khovanov Homology in $\mathbb{R}^3\times I$. https://arxiv.org/abs/2410.23455

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