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

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

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 $\pi=-...

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Bibliographic Details
Main Authors: Migdail, Jacob, Wehrli, Stephan
Format: Journal Article
Language:English
Published: 30-10-2024
Subjects:
Mathematics - Geometric Topology
Online Access:Get full text
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Summary: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 $\pi=-1$, 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 $S^3\times I$.
DOI:10.48550/arxiv.2410.23455