Free ribbon lemma for surface-link
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918153905242112 |
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| author | Kawauchi, Akio |
| author_facet | Kawauchi, Akio |
| contents | A free surface-link is a surface-link whose fundamental group is a free group not necessarily meridian-based. Free ribbon lemma says that every free sphere-link in the 4-sphere is a ribbon sphere-link. Four different proofs of Free ribbon lemma are explained. The first proof is done in an earlier paper. The second proof is done by showing that there is an O2-handle basis of a ribbon surface-link. The third proof is done by removing the commuter relations from a Wirtinger presentation of a free group, which a paper on another proof of Free ribbon lemma complements. The fourth proof is given by the special case of the proof of the result that every free surface-link is a ribbon surface-link which is a stabilization of a free ribbon sphere-link. As a consequence, it is shown that a surface-link is a sublink of a free surface-link if and only if it is a stabilization of a ribbon sphere-link. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09281 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Free ribbon lemma for surface-link Kawauchi, Akio Geometric Topology Primary 57N13, Secondary 57Q45 A free surface-link is a surface-link whose fundamental group is a free group not necessarily meridian-based. Free ribbon lemma says that every free sphere-link in the 4-sphere is a ribbon sphere-link. Four different proofs of Free ribbon lemma are explained. The first proof is done in an earlier paper. The second proof is done by showing that there is an O2-handle basis of a ribbon surface-link. The third proof is done by removing the commuter relations from a Wirtinger presentation of a free group, which a paper on another proof of Free ribbon lemma complements. The fourth proof is given by the special case of the proof of the result that every free surface-link is a ribbon surface-link which is a stabilization of a free ribbon sphere-link. As a consequence, it is shown that a surface-link is a sublink of a free surface-link if and only if it is a stabilization of a ribbon sphere-link. |
| title | Free ribbon lemma for surface-link |
| topic | Geometric Topology Primary 57N13, Secondary 57Q45 |
| url | https://arxiv.org/abs/2412.09281 |