Linking numbers of Montesinos links

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 $$\sum _{k=1}^{\frac{|p|}{2}}(-1{)}^{\lfloor (2k-1)\frac{q}{p}\rfloor }.$$ 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.

13 pages, 9 figures