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.

arXiv comment30 pages, 19 figures, fixed some typos and improved exposition. To appear in AGT

References in corpus (14)

• Khovanov's homology for tangles and cobordisms
• Spiders for rank 2 Lie algebras
• Markov theorem for transversal links
• The universal sl3-link homology
• New Quantum Obstructions to Sliceness
• Deformations of colored sl(N) link homologies via foams
• The Markov Theorem for transverse knots
• Rasmussen's spectral sequences and the sl(N)-concordance invariants
• A note on Gornik's perturbation of Khovanov-Rozansky homology
• The foam and the matrix factorization sl3 link homologies are equivalent
• Ozsvath-Szabo and Rasmussen invariants of doubled knots
• On transverse invariants from Khovanov homology
• Upsilon-like concordance invariants from sl(n) knot cohomology
• On transverse invariants from Khovanov-type homologies