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

Carlo Collari

doi:10.2140/agt.2020.20.1729

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arXiv · 1806.00752

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

Carlo Collari

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Abstract

In this paper we will make use of the Mackaay-Vaz approach to the universal $\mathfrak{sl}_3$-homology to define a family of cycles (called $\beta_3$-invariants) which are transverse braid invariants. This family includes Wu's $\psi_{3}$-invariant. Furthermore, we analyse the vanishing of the homology classes of the $\beta_3$-invariants and relate it to the vanishing of Plamenevskaya's and Wu's invariants. Finally, we use the $\beta_3$-invariants to produce some Bennequin-type inequalities.

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Carlo Collari. 2018-06-03. Transverse link invariants from the deformations of Khovanov $\mathfrak{sl}_{3}$-homology. https://doi.org/10.2140/agt.2020.20.1729

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