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Testing Bi-orderability of Knot Groups

Published:2016-06-23
Printed: Sep 2016
Department of Mathematics, University of Manitoba, Winnipeg, MB, R3T 2N2
• Colin Desmarais,
Department of Mathematics, University of Manitoba, Winnipeg, MB, R3T 2N2
• Patrick Naylor,
Department of Pure Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1
 Format: LaTeX MathJax PDF

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 499 of the corresponding knot groups. With our methods we are able to deal with 191 more.
 Keywords: knots, fundamental groups, orderable groups
 MSC Classifications: 57M25 - Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27 - Invariants of knots and 3-manifolds 06F15 - Ordered groups [See also 20F60]

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