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.
Funding Statement
This work was partially funded by research grants from Colby College.
Citation
Qidong HE. Scott A. TAYLOR. "Links, bridge number, and width trees." J. Math. Soc. Japan 75 (1) 73 - 111, January, 2023. https://doi.org/10.2969/jmsj/86158615
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