Rasmussen's spectral sequences and the sl(N)-concordance invariants

Abstract

Combining known spectral sequences with a new spectral sequence relating reduced and unreduced sl(N)-homology yields a relationship between the Homflypt-homology of a knot and its sl(N)-concordance invariants. As an application, some of the sl(N)-concordance invariants are shown to be linearly independent.

20 pages, 7 figures. Second version: sharpened main theorem, added references, minor corrections. Third version: minor corrections, this corresponds to the published article

References in corpus (6)

• Floer homology and knot complements
• On the Khovanov and knot Floer homologies of quasi-alternating links
• Some differentials on Khovanov-Rozansky homology
• sl3-foam homology calculations
• The Khovanov-Rozansky Cohomology and Bennequin Inequalities
• The reduced HOMFLY-PT homology for the Conway and the Kinoshita-Terasaka knots

Cited by in corpus (20)

• New Quantum Obstructions to Sliceness
• Deformations of colored sl(N) link homologies via foams
• Framed instanton homology and concordance
• sl3-foam homology calculations
• Upsilon-like concordance invariants from sl(n) knot cohomology
• A survey of the homology cobordism group
• Slice-torus concordance invariants and Whitehead doubles of links
• Almost positive links are strongly quasipositive
• The upsilon invariant at 1 of 3-braid knots
• A hitchhiker's guide to Khovanov homology
• On Khovanov Homology and Related Invariants
• On the values taken by slice torus invariants
• Instantons, special cycles, and knot concordance
• A family of slice-torus invariants from the divisibility of Lee classes
• A family of link concordance invariants from perturbed sl(n) homology
• Rasmussen invariants of Whitehead doubles and other satellites
• Transverse link invariants from the deformations of Khovanov ${\mathfrak{sl}}_3$-homology
• Slice-torus link invariants, combinatorial invariants, and positivity conditions
• Foams, iterated wreath products, field extensions and Sylvester sums
• Concordance invariants and the Turaev genus