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

  title={Residual Torsion-Free Nilpotence, Bi-Orderability and Two-Bridge Links},
  author={John H. Johnson},
  journal={Canadian Journal of Mathematics},
  • 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…