Affiliation:
1. School of Mathematics, Monash University , VIC 3800, Australia
Abstract
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.
Publisher
Oxford University Press (OUP)
Cited by
2 articles.
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1. Torus Lorenz links obtained by full twists along torus links;Proceedings of the American Mathematical Society;2023-03-14
2. Hyperbolic twisted torus links;Geometriae Dedicata;2023-02-19