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Functoriality of Odd and Generalized Khovanov Homology in $\mathbb{R}^3\times I$
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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 $\pi=-1$, 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 $S^3\times I$.
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Cited by 1 Pith paper
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A module structure on odd Khovanov homology and the odd invariant for ribbon 2-knots
Reduced odd Khovanov homology is a module over Λ*H1(Σ(L)), implying n(F)=|H1(Σ(F))| for ribbon 2-knots and injectivity of ribbon concordances over Q and Z_{2^k}.
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