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Flow loops and quantum groups

  • Sunghyuk Park
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@misc{park2026flow,
  title = {{Flow loops and quantum groups}},
  author = {Sunghyuk Park},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.21382},
  eprint = {2605.21382},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.21382},
}
RIS
TY  - UNPB
TI  - Flow loops and quantum groups
AU  - Sunghyuk Park
PY  - 2026
DA  - 2026/09/05
PB  - arXiv
DO  - 10.48550/arxiv.2605.21382
UR  - https://arxiv.org/abs/2605.21382
AB  - 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.
ER  -