{
  "abstract": "This paper is the second in a series of two which aims at introducing a new family of groups called $k$-shuffle braid groups, denoted $\\mathcal{B}_{n}(k)$. We focus here on the geometrical origins of these groups, as first observed by Calegari in arXiv:2105.11265. The spaces we are interested in are spaces of complex monic polynomials of degree $n$ whose critical values lie in $\\mathbb{C} \\setminus \\{1, e^{\\frac{2πi}{k}}, \\dots, e^{\\frac{2πi (k-1)}{k}}\\}$. We show that the $k$-shuffle braid groups are the fundamental groups of those spaces, which correspond geometrically to complements of $k$ translates of the discriminant variety. Moreover, we show that the $k$-shuffle braid groups $\\mathcal{B}_n(k)$ inject into the larger braid groups $\\mathcal{B}_{nk}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33890",
  "author_total": 1,
  "authors": [
    {
      "name": "Chloé Postel-Vinay"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/00w8dsfsx3ekp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33890",
  "fulltext_url": null,
  "id": "00w8dsfsx3ekp",
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  "landing_url": "https://arxiv.org/abs/2610.33890",
  "language": null,
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
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      "arxiv",
      "math.CV"
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      "arxiv",
      "math.GR"
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      "arxiv",
      "math.GT"
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      "openalex",
      "2608|Geometric and Algebraic Topology"
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  "openalex": "W7224013003",
  "pdf_url": "https://arxiv.org/pdf/2610.33890",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/00w8dsfsx3ekp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33890",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33890"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The geometric combinatorics of $k$-shuffle polynomials",
  "title_text": "The geometric combinatorics of k-shuffle polynomials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/00w8dsfsx3ekp",
  "venue": "arXiv",
  "versions": []
}