Blanchfield pairings and Gordian distance

TL;DR

This paper introduces a new lower bound for the Gordian distance between knots using the Blanchfield pairing, enabling the determination of Gordian distance for many complex prime knots.

Contribution

It presents a novel approach linking the Blanchfield pairing to Gordian distance, providing new tools for knot theory analysis.

Findings

Lower bound for Gordian distance established

Determined Gordian distance of 195 prime knots with up to 10 crossings

Most knots' Gordian distance was previously difficult to analyze

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 195 pairs of unoriented nontrivial prime knots with up to 10 crossings that their Gordian distance is equal to 3, most of which are difficult to treat otherwise.