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Session S28 - Knots, Surfaces, 3-manifolds

Wednesday, July 14, 19:20 ~ 19:50 UTC-3

Satellites and Lorenz knots

Jessica Purcell

Monash University, Australia   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

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.

Joint work with Thiago de Paiva (Monash University, Australia).

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