{
  "abstract": "We introduce the notion of mixed configuration spaces of the $3$-ball. That is, we consider both distinct circles and distinct points in the interior of the $3$-ball and we prove that the projection onto the configuration space of circles of the $3$-ball is a locally trivial fibration. The key idea for defining the mixed configuration spaces is to study fixed points of orientation-preserving homeomorphism of the $3$-ball that leave invariant a trivial link of $n$ components in the interior of the $3$-ball. In particular, we prove that two fixed points are Nielsen equivalent if and only if the associated loop braids are conjugate by an element of a distinguished free subgroup of rank $n$. This result stands as a $3$-dimensional counterpart of the $2$-dimensional result where fixed points of homeomorphisms of the punctured disc are characterized in terms of braid elements of the classical Artin braid group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04382",
  "author_total": 1,
  "authors": [
    {
      "name": "Stavroula Makri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ddm7e42zdr62g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04382",
  "fulltext_url": null,
  "id": "ddm7e42zdr62g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04382",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7220724962",
  "pdf_url": "https://arxiv.org/pdf/2610.04382",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ddm7e42zdr62g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04382",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04382"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Mixed configuration spaces, fixed points and Loop braid groups",
  "title_text": "Mixed configuration spaces, fixed points and Loop braid groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/ddm7e42zdr62g",
  "venue": "arXiv",
  "versions": []
}