Satellites and Lorenz knots

2021/03/17 by de Paiva, Thiago, Purcell, Jessica S.
#57K10 #57K32 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2103.09500

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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