Links, bridge number, and width trees
Abstract
To each link $L$ in $S^3$ we associate a collection of certain labelled directed trees, called width trees. We interpret some classical and new topological link invariants in terms of these width trees and show how the geometric structure of the width trees can bound the values of these invariants from below. We also show that each width tree is associated with a knot in $S^3$ and that if it also meets a high enough "distance threshold" it is, up to a certain equivalence, the unique width tree realizing the invariants.
 Publication:

arXiv eprints
 Pub Date:
 May 2020
 DOI:
 10.48550/arXiv.2005.12388
 arXiv:
 arXiv:2005.12388
 Bibcode:
 2020arXiv200512388H
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Combinatorics
 EPrint:
 Introduction expanded and additional examples added. This version has been accepted by J. Math. Soc. Japan