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PreprintCC BY 4.0arXiv

The Colored Jones Function does not determine any colored Links--Gould polynomial

  • Matthew Harper
  • Ben-Michael Kohli
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Abstract

We prove that there is no uniform description of LG(n) in terms of colored Jones polynomials for all knots, even when allowing infinitely many colors and arbitrary operations. We prove the n=1 case, using an existing cabling formula and the separation of the Conway and Kinoshita--Terasaka knots by LG(2). We develop an odd cabling formula and use a Vandermonde argument to show that for each n≥ 2 some satellite of each of these knots is distinguished by LG(n).

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Cite

BibTeXRIS
BibTeX
@misc{harper2026colored,
  title = {{The Colored Jones Function does not determine any colored Links--Gould polynomial}},
  author = {Matthew Harper and Ben-Michael Kohli},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12352},
  eprint = {2610.12352},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12352},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Colored Jones Function does not determine any colored Links--Gould polynomial
AU  - Matthew Harper
AU  - Ben-Michael Kohli
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.12352
UR  - https://arxiv.org/abs/2610.12352
AB  - We prove that there is no uniform description of LG^(n) in terms of colored Jones polynomials for all knots, even when allowing infinitely many colors and arbitrary operations. We prove the n=1 case, using an existing cabling formula and the separation of the Conway and Kinoshita--Terasaka knots by LG^(2). We develop an odd cabling formula and use a Vandermonde argument to show that for each n≥ 2 some satellite of each of these knots is distinguished by LG^(n).
ER  -