On the quantum $\mathfrak{sl}_3$ invariant of positive links

Matthew Harper; Efstratia Kalfagianni

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arXiv · 2508.15153

On the quantum $\mathfrak{sl}_3$ invariant of positive links

Matthew Harper·Efstratia Kalfagianni

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Abstract

We use the skein theory of $\mathfrak{sl}_3$-webs to study the properties of the quantum $\mathfrak{sl}_3$-link polynomial of positive links. We give explicit formulae for the three leading terms of the polynomial on positive links in terms of diagrammatic quantities of their positive diagrams. We show that a positive link is fibered if and only the second coefficient of the polynomial is equal to one. We also show that the third coefficient provides obstructions to representing links by positive braids.

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Matthew Harper, Efstratia Kalfagianni. 2025-08-21. On the quantum $\mathfrak{sl}_3$ invariant of positive links. https://arxiv.org/abs/2508.15153

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