This work demonstrates a cabling formula for the links--gould polynomial of knots, suggesting new genus bounds and implications for the v_n polynomial.
We give a cabling formula for the Links--Gould polynomial of knots colored with a $4n$-dimensional irreducible representation of UHqsl(2|1) and identify them with the Vₙ-polynomial of knots for $n=2$. Using the cabling formula, we obtain genus bounds and a specialization to the Alexander polynomial for the colored Links--Gould polynomial that is independent of n, which implies corresponding properties of the Vₙ-polynomial for $n=2$ conjectured in previous work of two of the authors, and extends the work done for $n=1$. Combined with work of one of the authors arXiv:2409.03557, our genus bound for LG⁽²⁾=V₂ is sharp for all knots with up to $16$ crossings.
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Garoufalidis et al. (2025) studied this question.
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