Transverse knots and Khovanov homology. (English) Zbl 1143.57006

An invariant of transverse links in the three-sphere equipped with the standard contact structure is defined as a distinguished element of the Khovanov homology of the link, via a resolution of a closed (transverse) braid representative. The quantum grading of the invariant is the self-linking number of the link. It is shown that for quasi-positive braids the invariant is non-zero, primitive and non-torsion, whereas it vanishes after transverse stabilization. A bound on the self-linking number is given in terms of Rasmussen’s invariant. Connections with Heegaard-Floer invariants are discussed.


57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
57R17 Symplectic and contact topology in high or arbitrary dimension
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