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PreprintCC BY 4.0arXiv

The top coefficient of the Links-Gould invariant is Murasugi-sum multiplicative

  • Cristina Anghel
  • Daniel López Neumann
  • Roland van der Veen
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Abstract

We prove that the Laurent polynomial in ℤ[q± 1] that is the top coefficient of the Links-Gould invariant of the boundary of a Seifert surface is multiplicative under arbitrary Murasugi sums of minimal genus Seifert surfaces. This extends a previous result of the second and third authors which only holds for plumbing, i.e. 4-Murasugi sum. Our technique relies on quantum supergroup themselves and PBW basis rather than the skein relations used in the previous work.

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Cite

BibTeXRIS
BibTeX
@misc{anghel2026coefficient,
  title = {{The top coefficient of the Links-Gould invariant is Murasugi-sum multiplicative}},
  author = {Cristina Anghel and Daniel López Neumann and Roland van der Veen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.09354},
  eprint = {2610.09354},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.09354},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The top coefficient of the Links-Gould invariant is Murasugi-sum multiplicative
AU  - Cristina Anghel
AU  - Daniel López Neumann
AU  - Roland van der Veen
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.09354
UR  - https://arxiv.org/abs/2610.09354
AB  - We prove that the Laurent polynomial in ℤ[q^± 1] that is the top coefficient of the Links-Gould invariant of the boundary of a Seifert surface is multiplicative under arbitrary Murasugi sums of minimal genus Seifert surfaces. This extends a previous result of the second and third authors which only holds for plumbing, i.e. 4-Murasugi sum. Our technique relies on quantum supergroup themselves and PBW basis rather than the skein relations used in the previous work.
ER  -