{
  "abstract": "The linking number and coefficients of the Conway polynomial are two examples of finite type invariants. Goussarov-Polyak-Viro proved that any finite type knot invariant can be computed in a two step process, where the second step is referred to as the GPV map for the invariant. This paper computes the GPV maps for the linking number and low-degree coefficients of the Conway Polynomial. Chmutov-Khoury-Rossi gave one description of the GPV maps for coefficients of the Conway polynomial in terms of arrow diagrams and state-sum calculations. We take a much more grounded approach using fundamental linear algebra to describe the GPV maps in terms of a basis for the vector space of Gauss diagrams.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20413",
  "author_total": 2,
  "authors": [
    {
      "name": "Nancy Scherich"
    },
    {
      "name": "Nathaniel Song"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5zmxj95wh67fd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20413",
  "fulltext_url": null,
  "id": "5zmxj95wh67fd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20413",
  "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": "W7213605419",
  "pdf_url": "https://arxiv.org/pdf/2609.20413",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5zmxj95wh67fd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20413",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20413"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Combinatorial Goussarov-Polyak-Viro Formulas for the Linking Number and Low Degree Coefficients of the Conway Polynomial",
  "title_text": "Combinatorial Goussarov-Polyak-Viro Formulas for the Linking Number and Low Degree Coefficients of the Conway Polynomial",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/5zmxj95wh67fd",
  "venue": "arXiv",
  "versions": []
}