The Alexander-polynomial normalization of the link series

Let LS3L\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

limt1limq1FLt(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.

Sources & referencesView supporting material

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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