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PreprintCC BY-NC-ND 4.0HAL

Higher order unknotting numbers for knots and links

  • Jean-Baptiste Meilhan
  • Harumi Ogita
  • Akira Yasuhara
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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 ≤ n. We generalize this result in three directions. First, we prove an analogous result for all higher order unknotting number given by Cn-moves. Second, we give several extensions to the link case. Third, we show that a similar result holds for ribbon 2-knots.

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Cite

BibTeXRIS
BibTeX
@misc{meilhan2026higher,
  title = {{Higher order unknotting numbers for knots and links}},
  author = {Jean-Baptiste Meilhan and Harumi Ogita and Akira Yasuhara},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39474},
  eprint = {2610.39474},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05844960v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Higher order unknotting numbers for knots and links
AU  - Jean-Baptiste Meilhan
AU  - Harumi Ogita
AU  - Akira Yasuhara
PY  - 2026
DA  - 2026/10/29
PB  - HAL
DO  - 10.48550/arxiv.2610.39474
UR  - https://hal.science/hal-05844960v1
AB  - 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 ≤ 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.
ER  -