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Residual torsion-free nilpotence, bi-orderability, and two-bridge links

Published online by Cambridge University Press:  25 January 2023

Jonathan Johnson*
Department of Mathematics, Oklahoma State University, Stillwater, OK, USA


Residual torsion-free nilpotence has proved to be an important property for knot groups with applications to bi-orderability and ribbon concordance. Mayland proposed a strategy to show that a two-bridge knot group has a commutator subgroup which is a union of an ascending chain of para-free groups. This paper proves Mayland’s assertion and expands the result to the subgroups of two-bridge link groups that correspond to the kernels of maps to $\mathbb{Z}$ . We call these kernels the Alexander subgroups of the links. As a result, we show the bi-orderability of a large family of two-bridge link groups. This proof makes use of a modified version of a graph-theoretic construction of Hirasawa and Murasugi in order to understand the structure of the Alexander subgroup for a two-bridge link group.

© The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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The work was supported by NSF grants DMS-1937215 and DMS-2213213.


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