Recursive Morse matchings compute integral Khovanov homology for all 4-strand torus links with at least 28 strands, including abundant 4-torsion and agreement with the Gorsky-Oblomkov-Rasmussen conjecture at infinity.
On the Khovanov and knot Floer homologies of quasi-alternating links
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abstract
Quasi-alternating links are a natural generalization of alternating links. In this paper, we show that quasi-alternating links are "homologically thin" for both Khovanov homology and knot Floer homology. In particular, their bigraded homology groups are determined by the signature of the link, together with the Euler characteristic of the respective homology (i.e. the Jones or the Alexander polynomial). The proofs use the exact triangles relating the homology of a link with the homologies of its two resolutions at a crossing.
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Morse matchings and Khovanov homology of 4-strand torus links
Recursive Morse matchings compute integral Khovanov homology for all 4-strand torus links with at least 28 strands, including abundant 4-torsion and agreement with the Gorsky-Oblomkov-Rasmussen conjecture at infinity.