2025/05/02 by Adnan, Thiago de Paiva, de Paiva, Thiago +2 · 1 citation
Engineering · Mathematics · #20B05 #57K10 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Metal Forming Simulation Techniques
paper · pdf · doi:10.48550/arxiv.2505.01021
openalex publication_date 2025/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Twisted torus links T(p,q;r,s) generalize torus links by introducing s additional twists on r adjacent strands of the torus link T(p,q). It is well known that the number of components of a torus link T(p, q) is given by the greatest common divisor of p and q. However, determining the number of components of twisted torus links is not as straightforward based solely on their parameters. In this work, we present a Euclidean algorithm-like procedure for computing the number of components of twisted torus links based on their parameters. As a result, we show that the number of components of a twisted torus link T(p, q; r, s) is a multiple of gcd(p, q, r, s), and in particular, T(p, q; r, s) is a knot only if gcd(p, q, r, s) = 1. We also use our algorithm to prove several conjectures related to the number of components in twisted torus links.