Flow loops and quantum groups

Sunghyuk Park

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arXiv · 2605.21382

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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BibTeX RIS

Sunghyuk Park. 2026-05-20. Flow loops and quantum groups. https://arxiv.org/abs/2605.21382

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