Twisted torus links that are unlinks

TL;DR

This paper classifies all parameter families of twisted torus links that result in unlinks, providing a complete characterization of when these complex links simplify to trivial unlinks.

Contribution

It offers a comprehensive classification of twisted torus links that are unlinks, filling a gap in the understanding of their topological properties.

Findings

Identifies all parameter sets where twisted torus links are unlinks

Provides a complete characterization of unlinked twisted torus links

Enhances understanding of link simplification conditions

Abstract

A twisted torus link $T(p,q,r,s)$ is obtained by performing $s$ full twists on $r$ adjacent strands of the $(p,q)$-torus link. In this paper, we classify twisted torus links that are unlinks. We give a complete characterization of all parameter families $(p,q,r,s)$ for which the associated twisted torus link is an unlink.