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

created by collari on 18 Sep 2018
modified on 08 Sep 2019

[BibTeX]

Accepted Paper

Inserted: 18 sep 2018
Last Updated: 8 sep 2019

Journal: Algebraic & Geometric Topology
Year: 2018

ArXiv: 1806.00752 PDF

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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