The $\mathrm{FK}_3$ knot polynomial

Stavros Garoufalidis; Shana Yunsheng Li

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arXiv · 2609.01506

The $\mathrm{FK}_3$ knot polynomial

Stavros Garoufalidis·Shana Yunsheng Li

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Abstract

We present the knot polynomial associated to the 12-dimensional sporadic Nichols algebra $\mathrm{FK}_3$ with automorphism, compute it for all knots with $\leq$ 16 crossings and discuss the found patterns. This knot polynomial is not a Vassiliev power series. We ponder how it compares to the knot polynomials that come from Lie algebras and their representations and what the other knot polynomials associated with the higher dimensional sporadic Nichols algebras are.

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Stavros Garoufalidis, Shana Yunsheng Li. 2026-09-01. The $\mathrm{FK}_3$ knot polynomial. https://arxiv.org/abs/2609.01506

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