Quantum invariants of 3-manifolds and links: a review
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915477335310336 |
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| author | Chae, John |
| author_facet | Chae, John |
| contents | We review the recent developments of quantum invariants of 3-manifolds and links: $\hat{Z}$ and $F_L$. They are $q$-series invariants originated from mathematical physics. They exhibit rich features, for example, quantum modularity, infinite dimensional Verma module structures and knot-quiver correspondence. Furthermore, they have connections to other topological invariants. We also provide a review of an extension of the above series invariants to Lie superalgebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02939 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum invariants of 3-manifolds and links: a review Chae, John Mathematical Physics High Energy Physics - Theory Geometric Topology Quantum Algebra We review the recent developments of quantum invariants of 3-manifolds and links: $\hat{Z}$ and $F_L$. They are $q$-series invariants originated from mathematical physics. They exhibit rich features, for example, quantum modularity, infinite dimensional Verma module structures and knot-quiver correspondence. Furthermore, they have connections to other topological invariants. We also provide a review of an extension of the above series invariants to Lie superalgebras. |
| title | Quantum invariants of 3-manifolds and links: a review |
| topic | Mathematical Physics High Energy Physics - Theory Geometric Topology Quantum Algebra |
| url | https://arxiv.org/abs/2509.02939 |