Ribbon knots, cabling, and handle decompositions

Jennifer Hom; Sungkyung Kang; JungHwan Park

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arXiv · 2003.02832

Ribbon knots, cabling, and handle decompositions

Jennifer Hom·Sungkyung Kang·JungHwan Park

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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.

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Jennifer Hom, Sungkyung Kang, JungHwan Park. 2020-03-05. Ribbon knots, cabling, and handle decompositions. https://arxiv.org/abs/2003.02832

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