Blanchfield pairings and Gordian distance

Abstract

A lower bound of the Gordian distance is presented in terms of the Blanchfield pairing. Our approach, in particular, allows us to show at least for [Formula: see text] pairs of unoriented nontrivial prime knots with up to [Formula: see text] crossings that their Gordian distance is equal to [Formula: see text], most of which are difficult to treat otherwise.