Ribbonness on boundary surface-link, revised
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914447118827520 |
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| author | Kawauchi, Akio |
| author_facet | Kawauchi, Akio |
| contents | A revised proof of the author's earlier result is given. It is shown that a boundary surface-link in the 4-sphere is a ribbon surface-link if the surface-link obtained from it by surgery along a pairwise nontrivial fusion 1-handle system is a ribbon surface-link. As a corollary, the surface-knot obtained from the anti-parallel surface-link of a non-ribbon surface-knot by surgery along a nontrivial or trivial fusion 1-handle is a non-ribbon or trivial surface-knot, respectively. This result answers Cochran's conjecture on non-ribbon sphere-knots in the affirmative. An application is made to construct an infinite family of non-ribbon surface links consisting of trivial components with at most one aspheric component. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18154 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ribbonness on boundary surface-link, revised Kawauchi, Akio Geometric Topology 57K45, 57K40 A revised proof of the author's earlier result is given. It is shown that a boundary surface-link in the 4-sphere is a ribbon surface-link if the surface-link obtained from it by surgery along a pairwise nontrivial fusion 1-handle system is a ribbon surface-link. As a corollary, the surface-knot obtained from the anti-parallel surface-link of a non-ribbon surface-knot by surgery along a nontrivial or trivial fusion 1-handle is a non-ribbon or trivial surface-knot, respectively. This result answers Cochran's conjecture on non-ribbon sphere-knots in the affirmative. An application is made to construct an infinite family of non-ribbon surface links consisting of trivial components with at most one aspheric component. |
| title | Ribbonness on boundary surface-link, revised |
| topic | Geometric Topology 57K45, 57K40 |
| url | https://arxiv.org/abs/2507.18154 |