Hyperbolic and satellite Lorenz links obtained by twisting

TL;DR

This paper classifies when certain Lorenz links, represented as T-links with full twists, are hyperbolic or satellite, providing a detailed geometric understanding of these links and their Dehn fillings.

Contribution

It offers a complete classification of hyperbolic parent links for T-links with full twists and presents effective hyperbolicity results for specific families, advancing the understanding of Lorenz link geometry.

Findings

Classified hyperbolic parent links for T-links with full twists

Provided effective hyperbolicity criteria for certain T-link families

Identified families of satellite T-links obtained by half-twists

Abstract

A Lorenz link is equivalent to a T-link, which is a positive braid built by concatenating torus braids of increasing size. When each torus braid except the largest is obtained by full twists, then the T-link can be described as the Dehn filling of a parent link. In this paper, we completely classify when such parent links are hyperbolic. This gives a classification of the geometry of T-links obtained by full twists when the amount of twisting is large, although the bound on the number of required twists is not effective. We also present effective results on hyperbolicity for two families of T-links obtained by twisting, even when the number of twists is small. Finally, we identify families of satellite T-links obtained by half-twists.