Hyperbolic Twisted Torus Links

TL;DR

This paper classifies all hyperbolic twisted torus links obtained by twisting strands of torus links more than three full times.

Contribution

It provides a complete classification of hyperbolic twisted torus links for certain twisting parameters.

Findings

Identifies all hyperbolic twisted torus links with |s| > 3.

Characterizes the conditions under which these links are hyperbolic.

Abstract

The twisted torus link $T(p, q; r, s)$ is obtained by twisting $r$ parallel strands of the $(p, q)$-torus link a total of $s$ full times. In this paper we find all twisted torus links which are hyperbolic for $\vert s\vert >3$.