On the tree-width of knot diagrams
Geometric Topology
2019-05-24 v2
Abstract
We show that a small tree-decomposition of a knot diagram induces a small sphere-decomposition of the corresponding knot. This, in turn, implies that the knot admits a small essential planar meridional surface or a small bridge sphere. We use this to give the first examples of knots where any diagram has high tree-width. This answers a question of Burton and of Makowsky and Mari\~no.
Keywords
Cite
@article{arxiv.1809.02172,
title = {On the tree-width of knot diagrams},
author = {Arnaud de Mesmay and Jessica Purcell and Saul Schleimer and Eric Sedgwick},
journal= {arXiv preprint arXiv:1809.02172},
year = {2019}
}
Comments
14 pages, 6 figures. V2: Minor updates to exposition