{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.21382",
  "author_total": 1,
  "authors": [
    {
      "name": "Sunghyuk Park"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0jqsmc73qneya.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.21382",
  "fulltext_url": null,
  "id": "0jqsmc73qneya",
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  "landing_url": "https://arxiv.org/abs/2605.21382",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "arxiv",
      "math.DS"
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      "arxiv",
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  "openalex": "W7161946140",
  "pdf_url": "https://arxiv.org/pdf/2605.21382",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0jqsmc73qneya.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2605.21382",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.21382"
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  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Flow loops and quantum groups",
  "title_text": "Flow loops and quantum groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/0jqsmc73qneya",
  "venue": "arXiv",
  "versions": []
}