Satellites and lorenz knots

Thiago De Paiva; Jessica S. Purcell

doi:10.1093/imrn/rnac335

Satellites and lorenz knots

Thiago De Paiva, Jessica S. Purcell

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

3 Citations (Scopus)

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.

Original language	English
Pages (from-to)	16540-16573
Number of pages	34
Journal	International Mathematics Research Notices
Volume	2023
Issue number	19
DOIs	https://doi.org/10.1093/imrn/rnac335
Publication status	Published - 1 Oct 2023

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10.1093/imrn/rnac335Licence: CC BY

Cite this

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Satellites and lorenz knots

Abstract

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Connections in low-dimensional topology

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Satellites and lorenz knots

Abstract

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Connections in low-dimensional topology

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