Skeins, $q$-series, and modularity
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918305022869504 |
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| author | Park, Sunghyuk |
| author_facet | Park, Sunghyuk |
| contents | 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, which suggests a new approach to Langlands duality for skein modules through $q$-series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18042 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Skeins, $q$-series, and modularity Park, Sunghyuk Geometric Topology High Energy Physics - Theory Number Theory Quantum Algebra Primary 57K31, 57K16, Secondary 33D80 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, which suggests a new approach to Langlands duality for skein modules through $q$-series. |
| title | Skeins, $q$-series, and modularity |
| topic | Geometric Topology High Energy Physics - Theory Number Theory Quantum Algebra Primary 57K31, 57K16, Secondary 33D80 |
| url | https://arxiv.org/abs/2601.18042 |