{
  "abstract": "The category TFS of thin flat surfaces, introduced by Khovanov, Qi, and Rozansky, is a strict symmetric monoidal category whose morphisms are compact oriented surfaces with corners arising as neighbourhoods of immersed graphs in a strip. We prove two main results. First, a normal form theorem: every connected viewable tf-cobordism is equal, in TFS, to a canonical composite determined by its topological type. Second, a sufficiency theorem: we establish a list of relations in the TFS category which are sufficient, meaning that any two composites of generators representing the same tf-cobordism are related by a finite sequence of the listed relations. Together, these results give a complete generators-and-relations presentation of TFS.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27771",
  "author_total": 2,
  "authors": [
    {
      "name": "Jaime Herrera"
    },
    {
      "name": "Carmen Rovi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/58zdm2s6xt3qt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27771",
  "fulltext_url": null,
  "id": "58zdm2s6xt3qt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27771",
  "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.AT"
    ],
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7204791240",
  "pdf_url": "https://arxiv.org/pdf/2608.27771",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/58zdm2s6xt3qt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.27771",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27771"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A normal form for the Thin Flat Surfaces category",
  "title_text": "A normal form for the Thin Flat Surfaces category",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/58zdm2s6xt3qt",
  "venue": "arXiv",
  "versions": []
}