{
  "abstract": "In this work, we construct a generalization of the $G_n^k$-theory to the case of an arbitrary hypergraph. The case of spherical braids is considered separately, using the stratification of the moduli space $\\mathcal{M}_n(S^2)$ and the hypergraph $Γ_n^{\\mathrm{sph}}$ encoding projective constraints. In contrast to the original $G_{n}^{k}$ theory, where codimension-one properties are determined by exactly $k$ particles, the present work considers various cases corresponding to strata of codimension~$1$. These groups admit nice maps to free products of cyclic groups. Among unsolved problems, we emphasize the question how the above construction works for abelian varieties and, in particular, for elliptic curves.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.07976",
  "author_total": 1,
  "authors": [
    {
      "name": "Vassily Olegovich Manturov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/556c5war8qqsy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.07976",
  "fulltext_url": null,
  "id": "556c5war8qqsy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.07976",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7202211131",
  "pdf_url": "https://arxiv.org/pdf/2608.07976",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/556c5war8qqsy.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:09Z",
      "native_id": "2608.07976",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.07976"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Generalizations of the groups $G_{n}^{k}$: graphs, moduli spaces, algebraic geometry, spherical braids",
  "title_text": "Generalizations of the groups G_n^k: graphs, moduli spaces, algebraic geometry, spherical braids",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/556c5war8qqsy",
  "venue": "arXiv",
  "versions": []
}