Satellite fully positive braid links are braided satellite of fully positive braid links
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915163694694400 |
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| author | Ito, Tetsuya |
| author_facet | Ito, Tetsuya |
| contents | A link in $S^{3}$ is a fully positive braid link if it is the closure of a positive braid that contains at least one full-twist. We show that a fully positive braid link is a satellite link if and only if it is the satellite of a fully positive braid link $C$ such that the pattern is a positive braid that contains sufficiently many full twists, where the number of necessary full twists only depends on $C$. As an application, we give a characterization of the unknot by the property that certain braided satellite is a (fully) positive braid knot. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01129 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Satellite fully positive braid links are braided satellite of fully positive braid links Ito, Tetsuya Geometric Topology A link in $S^{3}$ is a fully positive braid link if it is the closure of a positive braid that contains at least one full-twist. We show that a fully positive braid link is a satellite link if and only if it is the satellite of a fully positive braid link $C$ such that the pattern is a positive braid that contains sufficiently many full twists, where the number of necessary full twists only depends on $C$. As an application, we give a characterization of the unknot by the property that certain braided satellite is a (fully) positive braid knot. |
| title | Satellite fully positive braid links are braided satellite of fully positive braid links |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2402.01129 |