{
  "abstract": "By considering arc presentations and grid diagrams of satellite knots, we prove that if K is a satellite knot with companion C and wrapping number w, then its crossing number satisfies $c(K) \\geq \\frac{2}{5}(w^2c(C))^{1/11}$. We also prove other similar bounds regarding the crossing number and arc index of satellite knots and links. This is partial progress on Problem 1.2 of the K3 Problem List.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20900",
  "author_total": 1,
  "authors": [
    {
      "name": "Sam Ketchell"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7v6w1nx18mqe8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20900",
  "fulltext_url": null,
  "id": "7v6w1nx18mqe8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20900",
  "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": "W7213914974",
  "pdf_url": "https://arxiv.org/pdf/2609.20900",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7v6w1nx18mqe8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.20900",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20900"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Crossing Number and Arc Index of Satellite Knots",
  "title_text": "The Crossing Number and Arc Index of Satellite Knots",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/7v6w1nx18mqe8",
  "venue": "arXiv",
  "versions": []
}