On keen bridge splittings of links
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916096033947648 |
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| author | Ido, Ayako Jang, Yeonhee Kobayashi, Tsuyoshi |
| author_facet | Ido, Ayako Jang, Yeonhee Kobayashi, Tsuyoshi |
| contents | In this paper, we extend the concept of {\it (strongly) keenness} for Heegaard splittings to bridge splittings, and show that, for any integers $g$, $b$ and $n$ with $g\ge 0$, $b\ge 1$, $n\ge 1$ except for $(g,b)=(0,1)$ and $(g,b,n)=(0,3,1)$, there exists a strongly keen $(g,b)$-splitting of a link with distance $n$. We also show that any $(0,3)$-splitting of a link with distance $1$ cannot be keen. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09662 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On keen bridge splittings of links Ido, Ayako Jang, Yeonhee Kobayashi, Tsuyoshi Geometric Topology In this paper, we extend the concept of {\it (strongly) keenness} for Heegaard splittings to bridge splittings, and show that, for any integers $g$, $b$ and $n$ with $g\ge 0$, $b\ge 1$, $n\ge 1$ except for $(g,b)=(0,1)$ and $(g,b,n)=(0,3,1)$, there exists a strongly keen $(g,b)$-splitting of a link with distance $n$. We also show that any $(0,3)$-splitting of a link with distance $1$ cannot be keen. |
| title | On keen bridge splittings of links |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2401.09662 |