Linking numbers of Montesinos links
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909139736723456 |
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| author | Kim, Hyoungjun No, Sungjong Yoo, Hyungkee |
| author_facet | Kim, Hyoungjun No, Sungjong Yoo, Hyungkee |
| contents | The linking number of an oriented two-component link is an invariant indicating how intertwined the two components are. Tuler proved that the linking number of a two-component rational $\frac{p}{q}$-link is $$\sum^{\frac{|p|}{2}}_{k=1} (-1)^{\big\lfloor (2k-1) \frac{q}{p} \big\rfloor }.$$ In this paper, we provide a simple proof the above result, and introduce the numerical algorithm to find linking numbers of rational links. Using this result, we find linking numbers between any two components in a Montesinos link. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11512 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linking numbers of Montesinos links Kim, Hyoungjun No, Sungjong Yoo, Hyungkee Geometric Topology 57K10 The linking number of an oriented two-component link is an invariant indicating how intertwined the two components are. Tuler proved that the linking number of a two-component rational $\frac{p}{q}$-link is $$\sum^{\frac{|p|}{2}}_{k=1} (-1)^{\big\lfloor (2k-1) \frac{q}{p} \big\rfloor }.$$ In this paper, we provide a simple proof the above result, and introduce the numerical algorithm to find linking numbers of rational links. Using this result, we find linking numbers between any two components in a Montesinos link. |
| title | Linking numbers of Montesinos links |
| topic | Geometric Topology 57K10 |
| url | https://arxiv.org/abs/2403.11512 |