Flow loops and quantum groups
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917517031636992 |
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| author | Park, Sunghyuk |
| author_facet | Park, Sunghyuk |
| contents | This paper connects two seemingly different ways of studying knots: quantum group invariants and the dynamics of Morse flows. For fibered knots, we define a two-variable series invariant by counting Morse flow loops in the complement. This dynamical series is conjectured to agree with the BPS $q$-series of the knot complement, which arises from Verma modules for quantum groups and encodes all colored Jones polynomials. We prove this correspondence for all braid-homogeneous knots. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21382 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Flow loops and quantum groups Park, Sunghyuk Geometric Topology Quantum Algebra Symplectic Geometry This paper connects two seemingly different ways of studying knots: quantum group invariants and the dynamics of Morse flows. For fibered knots, we define a two-variable series invariant by counting Morse flow loops in the complement. This dynamical series is conjectured to agree with the BPS $q$-series of the knot complement, which arises from Verma modules for quantum groups and encodes all colored Jones polynomials. We prove this correspondence for all braid-homogeneous knots. |
| title | Flow loops and quantum groups |
| topic | Geometric Topology Quantum Algebra Symplectic Geometry |
| url | https://arxiv.org/abs/2605.21382 |