English

Gordian Adjacency for Positive Braid Knots

Geometric Topology 2021-01-12 v2

Abstract

A knot K1K_1 is said to be Gordian adjacent to a knot K2K_2 if K1K_1 is an intermediate knot on an unknotting sequence of K2K_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.

Keywords

Cite

@article{arxiv.1910.02933,
  title  = {Gordian Adjacency for Positive Braid Knots},
  author = {Tolson H. Bell and David C. Luo and Luke Seaton and Samuel P. Serra},
  journal= {arXiv preprint arXiv:1910.02933},
  year   = {2021}
}

Comments

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

R2 v1 2026-06-23T11:36:42.014Z