Blanchfield forms and Gordian distance

Abstract

Given a link in $S^3$ we will use invariants derived from the Alexander module and the Blanchfield pairing to obtain lower bounds on the Gordian distance between links, the unlinking number and various splitting numbers. These lower bounds generalise results recently obtained by Kawauchi.

We give an application restricting the knot types which can arise from a sequence of splitting operations on a link. This allows us to answer a question asked by Colin Adams in 1996.