Links with splitting number one

TL;DR

This paper introduces an algorithm to identify crossing changes that can split a link into separate components, also determining if the unlinking number is one, under mild conditions.

Contribution

It presents a novel algorithm that detects crossing changes leading to split links and computes the unlinking number for links.

Findings

Algorithm successfully identifies crossing changes for splitting links.

Complete list of crossing changes provided by the algorithm.

Determines whether the unlinking number of a link is one.

Abstract

We provide an algorithm to determine whether a link L admits a crossing change that turns it into a split link, under some fairly mild hypotheses on L. The algorithm also provides a complete list of all such crossing changes. It can therefore also determine whether the unlinking number of L is 1.