Knot cobordism and Lee's perturbation of Khovanov homology

TL;DR

This paper establishes a relationship between knot cobordisms, Lee's perturbation of Khovanov homology, and the band-unlinking number, providing new bounds based on torsion orders.

Contribution

It introduces an inequality linking cobordism features with torsion orders of Lee's perturbed Khovanov homology, offering a novel lower bound for the band-unlinking number.

Findings

Torsion order provides a lower bound for the band-unlinking number.

An inequality relates local maxima, genus, and torsion orders in knot cobordisms.

The results connect cobordism topology with algebraic invariants of knots.

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.