Non-bi-orderability of $6_2$ and $7_6$

TL;DR

This paper proves that the knot groups of knots $6_2$ and $7_6$ are not bi-orderable, filling a gap in the understanding of knot group orderability for knots with up to 7 crossings.

Contribution

It establishes non-bi-orderability for the remaining two knots with up to 7 crossings whose status was previously unknown.

Findings

Knot groups of $6_2$ and $7_6$ are not bi-orderable.

Method applies broadly to a class of knots.

Completes classification of bi-orderability for knots up to 7 crossings.

Abstract

We prove that the knot groups of $6_2$ and $7_6$ are not bi-orderable. These are the only two knot groups up to 7 crossings whose bi-orderability was not known. Our method applies to a very broad class of knots.