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Article

Ribbonness of a Stable-Ribbon Surface-Link, II: General Case

Osaka Central Advanced Mathematical Institute, Osaka Metropolitan University, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan
Mathematics 2025, 13(3), 402; https://doi.org/10.3390/math13030402
Submission received: 28 November 2024 / Revised: 6 January 2025 / Accepted: 24 January 2025 / Published: 25 January 2025

Abstract

It is shown that any handle-irreducible summand of every stable-ribbon surface-link is a unique ribbon surface-link up to equivalences so that every stable-ribbon surface-link is a ribbon surface-link. This is a generalization of a previously observed result for a stably trivial surface-link. Two observations are given. One observation is that a connected sum of two surface-links is a ribbon surface-link if and only if both the connected summands are ribbon surface-links. The other observation is a characterization of when a surface-link consisting of ribbon surface-knot components becomes a ribbon surface-link.
Keywords: ribbon surface-link; stable-ribbon surface-link; trivial surface-link; connected sum; O2-handle pair; uniqueness; SUPH system ribbon surface-link; stable-ribbon surface-link; trivial surface-link; connected sum; O2-handle pair; uniqueness; SUPH system

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MDPI and ACS Style

Kawauchi, A. Ribbonness of a Stable-Ribbon Surface-Link, II: General Case. Mathematics 2025, 13, 402. https://doi.org/10.3390/math13030402

AMA Style

Kawauchi A. Ribbonness of a Stable-Ribbon Surface-Link, II: General Case. Mathematics. 2025; 13(3):402. https://doi.org/10.3390/math13030402

Chicago/Turabian Style

Kawauchi, Akio. 2025. "Ribbonness of a Stable-Ribbon Surface-Link, II: General Case" Mathematics 13, no. 3: 402. https://doi.org/10.3390/math13030402

APA Style

Kawauchi, A. (2025). Ribbonness of a Stable-Ribbon Surface-Link, II: General Case. Mathematics, 13(3), 402. https://doi.org/10.3390/math13030402

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