Skeins, $q$-series, and modularity
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.
Fields of Study & Subjects
Geometric and Algebraic Topology
Algebraic structures and combinatorial models
Advanced Mathematical Identities
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 25 January 2026
- Document type
- Preprint