Testing bi-orderability of knot groups

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.

10 pages, 1 figure

References in corpus (2)

• Residual nilpotence and ordering in one-relator groups and knot groups
• Generalized torsion in knot groups

Cited by in corpus (3)

• Generalized torsion elements and bi-orderability of 3-manifold groups
• Residual Torsion-Free Nilpotence, Bi-Orderability and Pretzel Knots
• Ordered bases, order-preserving automorphisms and bi-orderable link groups