Linking numbers of Montesinos links

Hyoungjun Kim; Sungjong No; Hyungkee Yoo

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arXiv · 2403.11512

Linking numbers of Montesinos links

Hyoungjun Kim·Sungjong No·Hyungkee Yoo

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Abstract

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.

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BibTeX RIS

Hyoungjun Kim, Sungjong No, Hyungkee Yoo. 2024-03-18. Linking numbers of Montesinos links. https://arxiv.org/abs/2403.11512

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