Ribbon knots, cabling, and handle decompositions
Abstract
The fusion number of a ribbon knot is the minimal number of 1-handles needed to construct a ribbon disk. The strong homotopy fusion number of a ribbon knot is the minimal number of 2-handles in a handle decomposition of a ribbon disk complement. We demonstrate that these invariants behave completely differently under cabling by showing that the (p,1)-cable of any ribbon knot with fusion number one has strong homotopy fusion number one and fusion number p. Our main tools are Juh\'asz-Miller-Zemke's bound on fusion number coming from the torsion order of knot Floer homology and Hanselman-Watson's cabling formula for immersed curves.
Keywords
Cite
@article{arxiv.2003.02832,
title = {Ribbon knots, cabling, and handle decompositions},
author = {Jennifer Hom and Sungkyung Kang and JungHwan Park},
journal= {arXiv preprint arXiv:2003.02832},
year = {2020}
}
Comments
11 pages, 8 figures, Version 2: Minor changes to abstract and introduction. Added a reference to Meier and Zupan's work