Geodesic
Residual torsion-free nilpotence, bi-orderability, and two-bridge links
Canadian journal of mathematics, Tome 76 (2024) no. 2, pp. 394-457

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DOI

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.
DOI : 10.4153/S0008414X2300007X
Mots-clés : Two-bridge knots, residual nilpotence, bi-orderable groups, Alexander subgroups 
Johnson, Jonathan. Residual torsion-free nilpotence, bi-orderability, and two-bridge links. Canadian journal of mathematics, Tome 76 (2024) no. 2, pp. 394-457. doi: 10.4153/S0008414X2300007X
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