Knot cobordism and Lee’s perturbation of Khovanov homology

Abstract

For a connected cobordism [Formula: see text] between two knots [Formula: see text] in [Formula: see text], we establish an inequality involving the number of local maxima, the genus of [Formula: see text], and the torsion orders of [Formula: see text], where [Formula: see text] denotes Lee’s perturbation of Khovanov homology. This shows that the torsion order gives a lower bound for the band-unlinking number.