A plumbing-multiplicative function from the Links-Gould invariant

2025/02/18 by Daniel López-Neumann, Roland van der Veen, Lopez-Neumann, Daniel +1 · 3 citations
Mathematics · #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2502.12899

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 plumbing of surfaces. We deduce that the Links-Gould invariant of a fibred link in S³ is ℤ[q^{± 1}]-monic. As a purely topological application, we deduce a ``plumbing-uniqueness'' statement for links that bound surfaces obtained by plumbing/deplumbing unknotted twisted annuli as well as providing an obstruction for links to bound such surfaces.

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• U_q(\mathfrakgl(m|n)) bounds on the minimal genus of virtual links
• On some log-concavity properties of the Alexander-Conway and Links-Gould invariants
• On the colored Links--Gould polynomial

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