The Alexander-polynomial normalization of the link series

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Let L⊂S3L\subset S^3 be a framed oriented link with multivariable Alexander polynomial ∇L\nabla_L, and suppose ∇L\nabla_L is nonzero. Let FLtF_L^t be the regularized formal series associated with LL. The Alexander normalization conjecture. One has

lim⁡t→1lim⁡q→1FLt(qα1,…,qαV,q)∇L(qα1,…,qαV)=1.\lim_{t\to 1}\lim_{q\to 1}F_L^t(q^{\alpha_1},\ldots,q^{\alpha_V},q)\nabla_L(q^{\alpha_1},\ldots,q^{\alpha_V})=1.

This normalization is stated immediately after the link-level root-of-unity conjecture and is intended to relate the formal series to the multivariable Alexander polynomial. The supplied text gives no resolution status.

References

Primary source

Francesco Costantino, Sergei Gukov and Pavel Putrov, “Non-Semisimple TQFT's and BPS q-Series”, arXiv:2107.14238 (2023).

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