• DOI:10.4153/s0008414x2300007x
• Corpus ID: 235790793

Residual Torsion-Free Nilpotence, Bi-Orderability and Two-Bridge Links

@article{Johnson2019ResidualTN,
  title={Residual Torsion-Free Nilpotence, Bi-Orderability and Two-Bridge Links},
  author={John H. Johnson},
  journal={Canadian Journal of Mathematics},
  year={2019}
}

• John H. Johnson
• Published 18 December 2019
• Mathematics
• Canadian Journal of Mathematics

Residual torsion-free nilpotence has proven to be an important property for knot groups with applications to bi-orderability [11] and ribbon concordance [8]. Mayland [17] proposed a strategy to show that a two-bridge knot group has a commutator subgroup which is a union of an ascending chain of parafree 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 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 [9] in order to understand the structure of the Alexander subgroup for a two-bridge link group.