Geodesic
Bigrading the symplectic Khovanov cohomology
Cheng, Zhechi1
1 School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, China
Algebraic and Geometric Topology, Tome 23 (2023) no. 9, pp. 4057-4086

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We construct a well-defined relative second grading on symplectic Khovanov cohomology from holomorphic disc counting. We use a version of symplectic Khovanov cohomology defined for bridge diagrams rather than braids. We show that our second grading recovers the Jones grading of Khovanov homology up to an overall grading shift over any characteristic-zero field, through proving that the isomorphism of Abouzaid and Smith can be refined as an isomorphism between bigraded cohomology theories. The central idea of the proof is to construct an exact triangle for symplectic Khovanov cohomology that behaves similarly to the unoriented skein exact triangle for Khovanov homology.

DOI : 10.2140/agt.2023.23.4057
Keywords: Khovanov homology, Fukaya category, symplectic Khovanov cohomology, Hilbert scheme

Cheng, Zhechi 1

1 School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei, China 
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Cheng, Zhechi. Bigrading the symplectic Khovanov cohomology. Algebraic and Geometric Topology, Tome 23 (2023) no. 9, pp. 4057-4086. doi: 10.2140/agt.2023.23.4057

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