Gordian Adjacency for Positive Braid Knots
Geometric Topology
2021-01-12 v2
Abstract
A knot is said to be Gordian adjacent to a knot if is an intermediate knot on an unknotting sequence of . 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