Post #2400228
2026-04-27 05:18 UTC
A new knot invariant that “uniquely identifies more than 97% of the knots with 18 crossings. By comparison, the Jones polynomial, one of the most widely used invariants for cataloging knots, identifies about 42%, and the Alexander polynomial only about 11%.”
A great write-up in Quanta:
https://www.quantamagazine.org/a-powerful-new-qr-code-untangles-maths-knottiest-knots-20260422/
The paper itself is fun and fairly accessible. It’s also full of questions for the future!
“A Fast, Strong, Topologically Meaningful and Fun Knot Invariant” by Dror Bar-Natan, Roland van der Veen
https://arxiv.org/abs/2509.18456
Replies (2)
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@BoydStephenSmithJr@hachyderm.io 2026-04-27 05:32
@gregeganSF@mathstodon.xyz Is "number of crossings" well-defined? I thought humanity has recently shown that the crossing number isn't preserved by all topological operations.
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@f800gecko@mastodon.online 2026-04-27 13:09
@gregeganSF@mathstodon.xyz The resemblance of those drawings to this is kinda remarkable... "The Definitive Guide to Resistor Networks" - https://s.metamuffin.org/projects/resistor-networks.pdf [pic added so full d/l not necessary]