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Bull. Korean Math. Soc. 2024; 61(3): 779-784

Online first article May 16, 2024      Printed May 31, 2024

https://doi.org/10.4134/BKMS.b230373

Copyright © The Korean Mathematical Society.

An alternative proof for the minimality of strongly quasi-positive fibered knots in the ribbon concordance poset

Keiji Tagami

Hiroshima Shudo University

Abstract

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Baker proved that any strongly quasi-positive fibered knot is minimal with respect to the ribbon concordance among fibered knots in the three-sphere. By applying Rapaport's conjecture, which has been solved by Kochloukova, we can check that any strongly quasi-positive fibered knot is minimal with respect to the ribbon concordance among all knots in the three-sphere. In this short note, we give an alternative proof for the fact by utilizing the knot Floer homology.

Keywords: Strongly quasi-positive fibered knot, ribbon concordance

MSC numbers: 57K10

Supported by: The author was supported by JSPS KAKENHI Grant number JP22K13923.

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