Partial Classification of Lorenz Knots: Syllable Permutations of Torus Knots Words
Geometric Topology
2014-09-25 v2 Dynamical Systems
Abstract
We define families of aperiodic words associated to Lorenz knots that arise naturally as syllable permutations of symbolic words corresponding to torus knots. An algorithm to construct symbolic words of satellite Lorenz knots is defined. We prove, subject to the validity of a previous conjecture, that Lorenz knots coded by some of these families of words are hyperbolic, by showing that they are neither satellites nor torus knots and making use of Thurston's theorem. Infinite families of hyperbolic Lorenz knots are generated in this way, to our knowledge, for the first time. The techniques used can be generalized to study other families of Lorenz knots.
Keywords
Cite
@article{arxiv.1407.6341,
title = {Partial Classification of Lorenz Knots: Syllable Permutations of Torus Knots Words},
author = {Paulo Gomes and Nuno Franco and Luis Silva},
journal= {arXiv preprint arXiv:1407.6341},
year = {2014}
}