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Peer-reviewedCC BYQuantum Topology

A lower bound for the genus of a knot using the Links–Gould invariant

  • Ben-Michael Kohli1
  • Guillaume Tahar2
  1. 1Université de Genève, Switzerland
  2. 2Beijing Institute of Mathematical Sciences and Applications, P. R. China
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Abstract

The Links–Gould invariant of links LG^{2,1} is a two-variable generalization of the Alexander–Conway polynomial. Using representation theory of U_{q}\mathfrak{gl}(2 \vert 1) , we prove that the degree of the Links–Gould polynomial provides a lower bound on the Seifert genus of any knot, therefore improving the bound known as the Seifert inequality in the case of the Alexander polynomial. As an example, unlike some classical tools such as the Alexander polynomial and Levine–Tristram signature, this new genus bound detects the fact that the Kinoshita–Terasaka and Conway knots have genus greater than or equal to 2.

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Cite

BibTeXRIS
BibTeX
@article{kohli2026lower,
  title = {{A lower bound for the genus of a knot using the Links–Gould invariant}},
  author = {Ben-Michael Kohli and Guillaume Tahar},
  journal = {Quantum Topology},
  year = {2026},
  month = jun,
  doi = {10.4171/qt/263},
  url = {https://doi.org/10.4171/qt/263},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - A lower bound for the genus of a knot using the Links–Gould invariant
AU  - Ben-Michael Kohli
AU  - Guillaume Tahar
PY  - 2026
DA  - 2026/06/05
JO  - Quantum Topology
DO  - 10.4171/qt/263
UR  - https://doi.org/10.4171/qt/263
AB  - The Links–Gould invariant of links LG^{2,1} is a two-variable generalization of the Alexander–Conway polynomial. Using representation theory of U_{q}\mathfrak{gl}(2 \vert 1) , we prove that the degree of the Links–Gould polynomial provides a lower bound on the Seifert genus of any knot, therefore improving the bound known as the Seifert inequality in the case of the Alexander polynomial. As an example, unlike some classical tools such as the Alexander polynomial and Levine–Tristram signature, this new genus bound detects the fact that the Kinoshita–Terasaka and Conway knots have genus greater than or equal to 2.
SN  - 1663-487X
SN  - 1664-073X
ER  -