{
  "abstract": "A teardrop geodesic on a hyperbolic surface is a closed curve that is geodesic except at exactly one point, called its vertex. One imagines a closed curve with one point held down as it deforms to a geodesic. For each teardrop geodesic, we give an explicit geometric construction of the closed geodesic in its free homotopy class. This construction also yields a relation between the length of the teardrop geodesic, the angle at its vertex, and the length of its geodesic representative. We then apply the construction to a self-intersecting closed geodesic at a chosen self-intersection point. Since, at that point, the geodesic splits into two directed teardrop geodesics, our construction gives a geometric description of Turaev's cobracket in terms of geodesic representatives. Using this description we prove that if two self-intersection points yield a pair of canceling terms in the cobracket, then the angle at these points and the lengths of the small loops determined are the same.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17235",
  "author_total": 2,
  "authors": [
    {
      "name": "Moira Chas"
    },
    {
      "name": "Arpan Kabiraj"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3zx5vnq8nqxmr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17235",
  "fulltext_url": null,
  "id": "3zx5vnq8nqxmr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17235",
  "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": "W7221784794",
  "pdf_url": "https://arxiv.org/pdf/2610.17235",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3zx5vnq8nqxmr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17235",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17235"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Turaev cobracket, synthetic geometry and applications",
  "title_text": "Turaev cobracket, synthetic geometry and applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/3zx5vnq8nqxmr",
  "venue": "arXiv",
  "versions": []
}