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PreprintCC BY 4.0arXiv

The Links--Gould polynomial of an alternating link is alternating

  • Matthew Harper
  • Ben-Michael Kohli
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Abstract

Building on work of Kauffman--Saleur and earlier work of the second author, we derive a determinant formula for the Links--Gould polynomial of links. As an application, we prove a 20-year-old conjecture of Ishii: for any alternating link, the Links--Gould invariant is an alternating polynomial.

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Cite

BibTeXRIS
BibTeX
@misc{harper2026linksgould,
  title = {{The Links--Gould polynomial of an alternating link is alternating}},
  author = {Matthew Harper and Ben-Michael Kohli},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18803},
  eprint = {2610.18803},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18803},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Links--Gould polynomial of an alternating link is alternating
AU  - Matthew Harper
AU  - Ben-Michael Kohli
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.18803
UR  - https://arxiv.org/abs/2610.18803
AB  - Building on work of Kauffman--Saleur and earlier work of the second author, we derive a determinant formula for the Links--Gould polynomial of links. As an application, we prove a 20-year-old conjecture of Ishii: for any alternating link, the Links--Gould invariant is an alternating polynomial.
ER  -