Residual Torsion-Free Nilpotence and Two-Bridge Knot Groups

Geometry Topology Seminar
Monday, December 2, 2019 - 2:00pm for 1 hour (actually 50 minutes)
Jonathan Johnson – The University of Texas at Austin – jjohnson@math.utexas.edu
Miriam Kuzbary

I will discuss how a graph theoretic construction used by Hirasawa and Murasugi can be used to show that the commutator subgroup of the knot group of a two-bridge knot is a union of an ascending chain of parafree groups. Using a theorem of Baumslag, this implies that the commutator subgroup of a two-bridge knot group is residually torsion-free nilpotent which has applications to the anti-symmetry of ribbon concordance and the bi-orderability of two-bridge knots. In 1973, E. J. Mayland gave a conference talk in which he announced this result. Notes on this talk can be found online. However, this result has never been published, and there is evidence, in later papers, that a proper proof might have eluded Mayland.