Alternative proof of the ribbonness on classical link
Main Article Content
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
Article Details
Copyright (c) 2025 Kawauchi A.

This work is licensed under a Creative Commons Attribution 4.0 International License.
The International Journal of Physics Research and Applications is committed in making it easier for people to share and build upon the work of others while maintaining consistency with the rules of copyright. In order to use the Open Access paradigm to the maximum extent in true terms as free of charge online access along with usage right, we grant usage rights through the use of specific Creative Commons license.
License: Copyright © 2017 - 2025 | Open Access by International Journal of Physics Research and Applications is licensed under a Creative Commons Attribution 4.0 International License. Based on a work at Heighten Science Publications Inc.
With this license, the authors are allowed that after publishing with the journal, they can share their research by posting a free draft copy of their article to any repository or website.
Compliance 'CC BY' license helps in:
Permission to read and download | ✓ |
Permission to display in a repository | ✓ |
Permission to translate | ✓ |
Commercial uses of manuscript | ✓ |
'CC' stands for Creative Commons license. 'BY' symbolizes that users have provided attribution to the creator that the published manuscripts can be used or shared. This license allows for redistribution, commercial and non-commercial, as long as it is passed along unchanged and in whole, with credit to the author.
Please take in notification that Creative Commons user licenses are non-revocable. We recommend authors to check if their funding body requires a specific license.
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