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Transverse link invariants from the deformations of Khovanov $\mathfrak{sl}_{3}$–homology

Carlo Collari

Algebraic & Geometric Topology 20 (2020) 1729–1768

We make use of the Mackaay–Vaz approach to the universal 𝔰𝔩3 –homology to define a family of cycles (called β3 –invariants) which are transverse braid invariants. This family includes Wu’s ψ3 –invariant. Furthermore, we analyse the vanishing of the homology classes of the β3 –invariants and relate it to the vanishing of Plamenevskaya’s and Wu’s invariants. Finally, we use the β3 –invariants to produce some Bennequin-type inequalities.

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transverse invariants in $S^3$, Khovanov $\mathrm{sl}(3)$ homology, Plamenevskaya invariant
Mathematical Subject Classification 2010
Primary: 57M25, 57R17
Secondary: 57M27
Received: 14 June 2018
Revised: 4 June 2019
Accepted: 24 August 2019
Published: 20 July 2020
Carlo Collari
Alfréd Rényi Institute of Mathematics
New York University Abu Dhabi
Saadiyat Island
Abu Dhabi
United Arab Emirates