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Testing Bi-orderability of Knot Groups

Published online by Cambridge University Press:  20 November 2018

Adam Clay ,
Colin Desmarais  and
Patrick Naylor
Adam Clay
Affiliation:
Department of Mathematics, 420 Machray Hall, University of Manitoba, Winnipeg, MB, R3T 2N2 e-mail: adam.clay@umanitoba.ca e-mail: umdesmac@myumanitoba.ca
Colin Desmarais
Affiliation:
Department of Mathematics, 420 Machray Hall, University of Manitoba, Winnipeg, MB, R3T 2N2 e-mail: adam.clay@umanitoba.ca e-mail: umdesmac@myumanitoba.ca
Patrick Naylor
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1 e-mail: naylorp@myumanitoba.ca
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Abstract

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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

57M2557M2706F15knotsfundamental groupsorderable groups
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 3 , 01 September 2016 , pp. 472 - 482
Copyright
Copyright © Canadian Mathematical Society 2016

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