Satellites and Lorenz knots
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Publication:6142320
DOI10.1093/IMRN/RNAC335arXiv2103.09500OpenAlexW3138409180MaRDI QIDQ6142320
Jessica S. Purcell, Thiago de Paiva
Publication date: 25 January 2024
Published in: IMRN. International Mathematics Research Notices (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/2103.09500
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