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Residual torsion-free nilpotence, biorderability and pretzel knots

Jonathan Johnson

Algebraic & Geometric Topology 23 (2023) 1787–1830
Abstract

The residual torsion-free nilpotence of the commutator subgroup of a knot group has played a key role in studying the biorderability of knot groups. A technique developed by Mayland (1975) provides a sufficient condition for the commutator subgroup of a knot group to be residually torsion-free nilpotent using work of Baumslag (1967, 1969). 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 biorderable knot groups. These are the first examples of biorderable knot groups for knots which are not fibered or alternating.

Keywords
pretzel knots, biorderable, free factor, commutator subgroups of pretzel knots
Mathematical Subject Classification
Primary: 57K10
References
Publication
Received: 13 September 2020
Revised: 3 November 2021
Accepted: 7 December 2021
Published: 14 June 2023
Authors
Jonathan Johnson
Department of Mathematics
University of Texas at Austin
Austin, TX
United States

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