Torus Lorenz Links obtained by Full Twists along Torus Links

TL;DR

This paper investigates the geometric types of Lorenz links, specifically T-links obtained by full twists along torus links, revealing that such T-links are generally not torus links except for specific cases, thus addressing a question in knot theory.

Contribution

It proves that T-links formed by full twists along torus links are mostly not torus links, except in certain known cases, clarifying the structure of Lorenz links.

Findings

T-links from full twists are rarely torus links.

Most T-links obtained this way are hyperbolic or satellite.

Addresses a key question by Birman and Kofman.

Abstract

All knots are known to be hyperbolic, satellite, or torus knots, and one important family is Lorenz links, or T-links, which arise from dynamics. However, it remains difficult to determine the geometric type of a Lorenz link from a description via dynamics or as a T-link. In this paper, we consider those T-links that are torus links. We show that T-links obtained by full twists along torus links can never be torus links, aside from a family of cases. This addresses a question of Birman and Kofman.