The cabling formula for GM series

Let KK be a knot with a well-defined GM series, and let C(tp,sp)(K)C_{(tp,sp)}(K) denote its (tp,sp)(tp,sp)-cabling with gcd(s,t)=1\gcd(s,t)=1. Cabling Formula. The cabling formula above holds for any knot with a well-defined GM series, so long as the right-hand side converges. The source proves the formula for plumbed knots and conjectures its extension to arbitrary knots; convergence remains required.

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Primary source

Pedro Guicardi and Mrunmay Jagadale, “Z-TQFT, Surgery Formulas, and New Algebras”, arXiv:2509.14311 (2025).

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