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Ribbon knots, cabling, and handle decompositions

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Title
Ribbon knots, cabling, and handle decompositions
Author(s)
Hom, Jennifer; Sungkyung Kang; Park, JungHwan
Publication Date
2021-08
Journal
Mathematical Research Letters, v.28, no.5, pp.1441 - 1457
Publisher
International Press, Inc.
Abstract
© 2021 International Press of Boston, Inc.. All rights reserved.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 Juhász-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.
URI
https://pr.ibs.re.kr/handle/8788114/12766
DOI
10.4310/MRL.2021.V28.N5.A7
ISSN
1073-2780
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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