Testing bi-orderability of knot groups

TL;DR

This paper advances the understanding of bi-orderability in knot groups by applying recent theorems, significantly increasing the number of knots with known bi-orderability status among those with up to 12 crossings.

Contribution

The authors extend existing methods to determine bi-orderability of knot groups, analyzing all knots with up to 12 crossings and identifying 191 additional cases.

Findings

Bi-orderability determined for more knot groups.

Application of recent theorems improves analysis coverage.

Enhanced understanding of knot group properties.

Abstract

We investigate the bi-orderability of two-bridge knot groups and the groups of knots with 12 or fewer crossings by applying recent theorems of Chiswell, Glass and Wilson. Amongst all knots with 12 or fewer crossings (of which there are 2977), previous theorems were only able to determine bi-orderability of 599 of the corresponding knot groups. With our methods we are able to deal with 191 more.