The unknotting number and classical invariants I

Abstract

Given a knot K we introduce a new invariant coming from the Blanchfield pairing and we show that it gives a lower bound on the unknotting number of K. This lower bound subsumes the lower bounds given by the Levine-Tristram signatures, by the Nakanishi index and it also subsumes the Lickorish obstruction to the unknotting number being equal to one. Our approach in particular allows us to show for 25 knots with up to 12 crossings that their unknotting number is at least three, most of which are very difficult to treat otherwise.

43 pages

References in corpus (2)

• Knot Floer homology and the four-ball genus
• Knots with unknotting number 1 and essential Conway spheres

Cited by in corpus (8)

• The degree of the Alexander polynomial is an upper bound for the topological slice genus
• Embedded surfaces with infinite cyclic knot group
• An explicit computation of the Blanchfield pairing for arbitrary links
• On classical upper bounds for slice genera
• Twisted Blanchfield pairings and twisted signatures I: Algebraic background
• Positive braid knots of maximal topological 4-genus
• Gaps between consecutive untwisting numbers
• Twisted Blanchfield pairings and twisted signatures II: Relation to Casson-Gordon invariants