Skeins, $q$-series, and modularity

Sunghyuk Park

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arXiv · 2601.18042

Skeins, $q$-series, and modularity

Sunghyuk Park

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Abstract

We study BPS $q$-series associated to 3-manifolds decorated by a line defect along an embedded link. We prove that these $q$-series depend only on the class of the link in the skein module, thereby defining a homomorphism from the skein module to the space of $q$-series. The image of this homomorphism is conjectured to be holomorphically quantum modular, and we verify this conjecture in an explicit example.

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Sunghyuk Park. 2026-01-25. Skeins, $q$-series, and modularity. https://arxiv.org/abs/2601.18042

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