Khovanov homology and refined bounds for Gordian distances

Claudius Zibrowius; Laura Marino; Lukas Lewark

Khovanov homology and refined bounds for Gordian distances

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arxiv 2409.05743 v1 pith:6HMCILMI submitted 2024-09-09 math.GT math.QA

Lukas Lewark , Laura Marino , Claudius Zibrowius This is my paper · ORCID

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keywords boundsgordiandistancehomologyinvariantskhovanovboundcombines

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From Khovanov homology, we extract a new lower bound for the Gordian distance of knots, which combines and strengthens the previously existing bounds coming from Rasmussen invariants and from torsion invariants. We also improve the bounds for the proper rational Gordian distance.

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Morse matchings and Khovanov homology of 4-strand torus links
math.GT 2025-07 conditional novelty 7.0 of 10

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.

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