Residual Torsion-Free Nilpotence, Bi-Orderability and Pretzel Knots

Jonathan Johnson

doi:10.2140/agt.2023.23.1787

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arXiv · 2008.13353

Residual Torsion-Free Nilpotence, Bi-Orderability and Pretzel Knots

Jonathan Johnson

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Abstract

The residual torsion-free nilpotence of the commutator subgroup of a knot group has played a key role in studying the bi-orderability of knot groups. A technique developed by Mayland provides a sufficient condition for the commutator subgroup of a knot group to be residually-torsion-free nilpotent using work of Baumslag. In this paper, we apply Mayland's technique to several genus one pretzel knots and a family of pretzel knots with arbitrarily high genus. As a result, we obtain a large number of new examples of knots with bi-orderable knot groups. These are the first examples of bi-orderable knot groups for knots which are not fibered or alternating.

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Jonathan Johnson. 2020-08-31. Residual Torsion-Free Nilpotence, Bi-Orderability and Pretzel Knots. https://doi.org/10.2140/agt.2023.23.1787

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