{
  "abstract": "Links in projective space $\\mathbb{R}P^3$ can be represented by diagrams in $\\mathbb{R}P^2$ where the projective plane $\\mathbb{R}P^2$ is represented by a disk with antipodal identifications on the boundary. In this context if we place an $n-$strand braid $β$ on this disk keeping its end points on the boundary then due to the identification of antipodal points it naturally represents a link diagram in $\\mathbb{R}P^3$. We call this the projective closure of the braid $β$. In this paper we show that not all links in $\\mathbb{R}P^3$ possess a diagram represented by projective closure of some braid.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29058",
  "author_total": 3,
  "authors": [
    {
      "name": "Aakash Gupta"
    },
    {
      "name": "Louis H. Kauffman"
    },
    {
      "name": "Rama Mishra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8ycr27q6aqs36.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29058",
  "fulltext_url": null,
  "id": "8ycr27q6aqs36",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29058",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7214311859",
  "pdf_url": "https://arxiv.org/pdf/2609.29058",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8ycr27q6aqs36.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.29058",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29058"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Projective Braids in $\\mathbb{R}P^3$",
  "title_text": "Projective Braids in ℝP^3",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/8ycr27q6aqs36",
  "venue": "arXiv",
  "versions": []
}