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

Fuente: arXiv
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Main Authors: Migdail, Jacob, Wehrli, Stephan
Format: Preprint
Published: 2024
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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
id 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