Unlinking Numbers of Links with Crossing Number 10

TL;DR

This paper determines the unlinking numbers of most prime, non-split links with crossing number 10 by applying link invariants and crossing change analysis, extending previous methods used for links with fewer crossings.

Contribution

It computes the unlinking numbers for nearly all prime, non-split 10-crossing links, filling a gap in knot theory research.

Findings

Unlinking numbers for 285 of 287 links were determined.

Methods extend previous techniques used for links with fewer crossings.

Identified 2 links with unresolved unlinking numbers.

Abstract

In this paper we investigate the unlinking numbers of 10-crossing links. We make use of various link invariants and explore their behaviour when crossings are changed. The methods we describe have been used previously to compute unlinking numbers of links with crossing number at most 9. Ultimately, we find the unlinking numbers of all but 2 of the 287 prime, non-split links with crossing number 10.