Gordian Adjacency for Positive Braid Knots

Tolson H. Bell; David C. Luo; Luke Seaton; Samuel P. Serra

paper

Gordian Adjacency for Positive Braid Knots

arXiv:1910.02933

Abstract

A knot $K_{1}$ is said to be Gordian adjacent to a knot $K_{2}$ if $K_{1}$ is an intermediate knot on an unknotting sequence of $K_{2}$ . We extend previous results on Gordian adjacency by showing sufficient conditions for Gordian adjacency between classes of positive braid knots through manipulations of braid words. In addition, we explore unknotting sequences of positive braid knots and give a proof that there are only finitely many positive braid knots for a given unknotting number.

20 pages; to appear in Rose-Hulman Undergraduate Mathematics Journal