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PreprintarXiv licencearXiv

The FK3 knot polynomial

  • Stavros Garoufalidis
  • Shana Yunsheng Li
Open at sourcePDFDOICite

Abstract

We present the knot polynomial associated to the 12-dimensional sporadic Nichols algebra FK3 with automorphism, compute it for all knots with ≤ 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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Cite

BibTeXRIS
BibTeX
@misc{garoufalidis2026knot,
  title = {{The $\mathrmFK_3$ knot polynomial}},
  author = {Stavros Garoufalidis and Shana Yunsheng Li},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.01506},
  eprint = {2609.01506},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01506},
}
RIS
TY  - UNPB
TI  - The FK_3 knot polynomial
AU  - Stavros Garoufalidis
AU  - Shana Yunsheng Li
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.01506
UR  - https://arxiv.org/abs/2609.01506
AB  - We present the knot polynomial associated to the 12-dimensional sporadic Nichols algebra FK_3 with automorphism, compute it for all knots with ≤ 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.
ER  -