Satellites and Lorenz knots

Thiago de Paiva; Jessica S. Purcell

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arXiv · 2103.09500

Satellites and Lorenz knots

Thiago de Paiva·Jessica S. Purcell

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Abstract

We construct infinitely many families of Lorenz knots that are satellites but not cables, giving counterexamples to a conjecture attributed to Morton. We amend the conjecture to state that Lorenz knots that are satellite have companion a Lorenz knot, and pattern equivalent to a Lorenz knot. We show this amended conjecture holds very broadly: it is true for all Lorenz knots obtained by high Dehn filling on a parent link, and other examples.

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Thiago de Paiva, Jessica S. Purcell. 2021-03-17. Satellites and Lorenz knots. https://arxiv.org/abs/2103.09500

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