2024/03/18 by Hyoungjun Kim, Kim, Hyoungjun, Sungjong No +3
Mathematics · #Advanced Topics in Algebra #Advanced Differential Equations and Dynamical Systems #Commutative Algebra and Its Applications
paper · pdf · doi:10.48550/arxiv.2403.11512
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 (p)/(q)-link is ∑(|p|)/(2)k=1 (-1)\lfloor (2k-1) (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.