Three-page indices of torus links
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918097010556928 |
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| author | Jang, Useong Lee, Minseo Yoo, Hyungkee |
| author_facet | Jang, Useong Lee, Minseo Yoo, Hyungkee |
| contents | An arc presentation of a link is an embedding into the open book decomposition of $\mathbb{R}^3$ with a finite number of pages. An important rule of arc presentations is that different arcs must be placed on separate pages. In 1999, Dynnikov proposed a three-page presentation that bends this rule by restricting the total number of pages to three. Dynnikov showed that every link admits a three-page presentation. In this paper, we provide an alternative proof of this result. Also we define the three-page index $α_3(L)$ of a link $L$ that the minimum number of arcs needed to represent $L$ in a three-page presentation. We examine three-page presentations for torus links, leading to the determination of the exact three-page indices for several torus links. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13633 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Three-page indices of torus links Jang, Useong Lee, Minseo Yoo, Hyungkee Geometric Topology An arc presentation of a link is an embedding into the open book decomposition of $\mathbb{R}^3$ with a finite number of pages. An important rule of arc presentations is that different arcs must be placed on separate pages. In 1999, Dynnikov proposed a three-page presentation that bends this rule by restricting the total number of pages to three. Dynnikov showed that every link admits a three-page presentation. In this paper, we provide an alternative proof of this result. Also we define the three-page index $α_3(L)$ of a link $L$ that the minimum number of arcs needed to represent $L$ in a three-page presentation. We examine three-page presentations for torus links, leading to the determination of the exact three-page indices for several torus links. |
| title | Three-page indices of torus links |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2507.13633 |