Rasmussen's spectral sequences and the \(\mathfrak{sl}_N\)-concordance invariants

DOI10.1016/j.aim.2014.04.003zbMath1316.57007arXiv1310.3100OpenAlexW2086977260MaRDI QIDQ2452069

Lukas Lewark

Publication date: 28 May 2014

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.3100

zbMATH Keywords

spectral sequencesslice genusKhovanov-Rozansky homologiesRasmussen invariantsPretzel knotsslice-torus invariants

Mathematics Subject Classification ID

Related Items

On Khovanov Homology and Related Invariants ⋮ Upsilon-like concordance invariants from \(\mathfrak{s}\mathfrak{l}_n\) knot cohomology ⋮ \(\mathfrak{sl}_3\)-foam homology calculations ⋮ The upsilon invariant at 1 of 3-braid knots ⋮ Framed instanton homology and concordance ⋮ On the slice genus of generalized algebraic knots ⋮ A survey of the homology cobordism group ⋮ On the values taken by slice torus invariants ⋮ Almost positive links are strongly quasipositive ⋮ Slice-torus Concordance Invariants and Whitehead Doubles of Links ⋮ A note on the weak splitting number ⋮ Slice‐torus link invariants, combinatorial invariants and positivity conditions ⋮ New quantum obstructions to sliceness ⋮ Transverse link invariants from the deformations of Khovanov \(\mathfrak{sl}_3\)-homology

Uses Software

• Knotscape
• knotkit
• FoamHo

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(\mathfrak{sl}_3\)-foam homology calculations
• A note on Gornik's perturbation of Khovanov-Rozansky homology
• Concordance invariants from higher order covers
• On the Heegaard Floer homology of branched double-covers
• Khovanov homology and the slice genus
• A slice genus lower bound from \(sl(n)\) Khovanov-Rozansky homology
• The Rasmussen invariants and the sharper slice-Bennequin inequality on knots
• Khovanov-Rozansky homology of two-bridge knots and links
• An estimate of the Rasmussen invariant for links and the determination for certain links
• Some differentials on Khovanov-Rozansky homology
• Matrix factorizations and link homology. II.
• Ozsváth-Szabó and Rasmussen invariants of cable knots
• Man and machine thinking about the smooth 4-dimensional Poincaré conjecture
• On the quantum filtration of the Khovanov-Rozansky cohomology
• On the signature of a link
• Heegaard Floer homology and alternating knots
• \(\text{sl}(3)\) link homology
• Ribbon graphs and their invariants derived from quantum groups
• Computations of the Ozsvath-Szabo knot concordance invariant
• A categorification of the Jones polynomial
• Homologically thin, non-quasi-alternating links
• Correction to the article ``An infinite-rank summand of topologically slice knots
• Khovanov's homology for tangles and cobordisms
• A refinement of Rasmussen's \({s}\)-invariant
• Transverse knots and Khovanov homology
• The foam and the matrix factorization \(sl_3\) link homologies are equivalent
• Ozsváth-Szabó and Rasmussen invariants of doubled knots
• An endomorphism of the Khovanov invariant
• The rational Khovanov homology of 3-strand pretzel links
• Computable bounds for Rasmussen’s concordance invariant
• Quasipositivity as an obstruction to sliceness
• CALCULATING BAR-NATAN'S CHARACTERISTIC TWO KHOVANOV HOMOLOGY
• A REMARK ON RASMUSSEN'S INVARIANT OF KNOTS
• The Ozsváth-Szabó and Rasmussen concordance invariants are not equal
• NOTIONS OF POSITIVITY AND THE OZSVÁTH–SZABÓ CONCORDANCE INVARIANT
• Twisting quasi-alternating links
• Homogeneous Links
• The Rasmussen invariant of a homogeneous knot
• RASMUSSEN INVARIANT, SLICE-BENNEQUIN INEQUALITY, AND SLICENESS OF KNOTS
• Slice knots with distinct Ozsváth-Szabó and Rasmussen invariants
• A Concordance Invariant from the Floer Homology of Double Branched Covers
• Matrix factorizations and link homology
• On the Khovanov and knot Floer homologies of quasi-alternating links