Concordance invariants from $U(1) \times U(1)$-equivariant Khovanov homology

Rostislav Akhmechet; Melissa Zhang

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arXiv · 2210.10731

Concordance invariants from $U(1) \times U(1)$-equivariant Khovanov homology

Rostislav Akhmechet·Melissa Zhang

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Abstract

We study Khovanov homology over the Frobenius algebra $\mathbb{F}[U,V,X]/((X-U)(X-V))$, or $U(1) \times U(1)$-equivariant Khovanov homology, and extract two families of concordance invariants using the algebraic $U$-power and $V$-power filtrations on the chain complex. We also further develop the reduced version of the theory and study its behavior under mirroring.

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BibTeX RIS

Rostislav Akhmechet, Melissa Zhang. 2022-10-19. Concordance invariants from $U(1) \times U(1)$-equivariant Khovanov homology. https://arxiv.org/abs/2210.10731

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