{
  "abstract": "Ohyama, Taniyama and Yamada showed that finite type knot invariants are insensitive to the unknotting number: for any integer n and any knot K, there is an unknotting number 1 knot which cannot be distinguished from K by any finite type invariant of order $\\le n$. We generalize this result in three directions. First, we prove an analogous result for all higher order unknotting number given by $C_n$-moves. Second, we give several extensions to the link case. Third, we show that a similar result holds for ribbon 2-knots.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39474",
  "author_total": 3,
  "authors": [
    {
      "name": "Jean-Baptiste Meilhan"
    },
    {
      "name": "Harumi Ogita"
    },
    {
      "name": "Akira Yasuhara"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1pmrk5bys3qe4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39474",
  "fulltext_url": null,
  "id": "1pmrk5bys3qe4",
  "issns": [],
  "landing_url": "https://hal.science/hal-05844960v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GT"
    ],
    [
      "hal",
      "0.math"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39474",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1pmrk5bys3qe4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:03Z",
      "native_id": "hal-05844960",
      "source": "hal",
      "url": "https://hal.science/hal-05844960v1"
    },
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39474",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39474"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Higher order unknotting numbers for knots and links",
  "title_text": "Higher order unknotting numbers for knots and links",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/1pmrk5bys3qe4",
  "venue": "HAL",
  "versions": []
}