Alternative proof of the ribbonness on classical link
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Abstract
Alternative proof is given for an earlier presented result that if a link in 3-space bounds a compact oriented proper surface (without closed component) in the upper half 4-space, then the link bounds a ribbon surface in the upper half 4-space which is a boundary-relative renewal embedding of the original surface.
2020 Mathematics Subject Classification: Primary 57K45; Secondary 57K40
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Copyright (c) 2025 Kawauchi A.
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Kawauchi A, Shibuya T, Suzuki S. Descriptions on surfaces in four-space I: Normal forms. Math Semin Notes Kobe Univ. 1982;10:75–125. Available from: https://www.researchgate.net/publication/268176987_Descriptions_on_surfaces_in_four_space_I_Normal_forms
Kawauchi A. Ribbonness on classical link. J Math Tech Comput Math. 2023;2(8):375–7. Available from: https://doi.org/10.48550/arXiv.2307.16483
Fox RH. Some problems in knot theory. In: Topology of 3-manifolds and related topics. Engelwood Cliffs (NJ): Prentice-Hall, Inc.; 1962;168–76. Available from: https://ben300694.github.io/pdfs/concordance/%5BFox%5D_Some_Problems_in_Knot_Theory_(1962).pdf
Fox RH. Characterization of slices and ribbons. Osaka J Math. 1973;10:69–76.
Kawauchi A. A chord diagram of a ribbon surface-link. J Knot Theory Ramifications. 2015;24:1540002. Available from: https://doi.org/10.1142/S0218216515400027
Kawauchi A. Ribbonness of a stable-ribbon surface-link, I. A stably trivial surface-link. Topol Appl. 2021;301:107522. Available from: https://doi.org/10.1016/j.topol.2020.107522