Knot cobordism and Lee’s perturbation of Khovanov homology
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Publication:5076513
DOI10.1142/S0218216522500122zbMATH Open1494.57023arXiv2201.01910MaRDI QIDQ5076513
Publication date: 17 May 2022
Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)
Abstract: For a connected cobordism S between two knots K1,K2 in S3, we establish an inequality involving the number of local maxima, the genus of S, and the torsion orders of Kht(K1),Kht(K2), where Kht denotes Lee's perturbation of Khovanov homology. This shows that the torsion order gives a lower bound for the band-unlinking number.
Full work available at URL: https://arxiv.org/abs/2201.01910
Cobordism and concordance in PL-topology (57Q60) Homology theories in knot theory (Khovanov, Heegaard-Floer, etc.) (57K18)
Cites Work
- An invariant of link cobordisms from Khovanov homology
- A categorification of the Jones polynomial
- Ribbon distance and Khovanov homology
- Knot Floer homology obstructs ribbon concordance
- Khovanov's homology for tangles and cobordisms
- An endomorphism of the Khovanov invariant
- Khovanov homology and ribbon concordances
- Knot cobordisms, bridge index, and torsion in Floer homology
Related Items (2)
Knotted fields and explicit fibrations for lemniscate knots ⋮ The Karoubi envelope and Lee's degeneration of Khovanov homology
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