Transverse link invariants from the deformations of Khovanov ${\mathfrak{sl}}_3$-homology

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.

30 pages, 19 figures, fixed some typos and improved exposition. To appear in AGT