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arXiv · 2610.09354

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 $\mathbb{Z}[q^{\pm 1}]$ 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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Cristina Anghel, Daniel López Neumann, Roland van der Veen. 2026-10-07. The top coefficient of the Links-Gould invariant is Murasugi-sum multiplicative. https://arxiv.org/abs/2610.09354

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