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PreprintarXiv licencearXiv

Montesinos Knots with Delta-Unknotting Number One

  • Kazumichi Nakamura
Open at sourcePDFDOICite

Abstract

The Δ-unknotting number for a knot is defined as the minimum number of Δ-moves needed to deform the knot into the trivial knot. In this paper, we discuss Montesinos knots whose Δ-unknotting number is equal to one. We propose a conjectural characterization of Montesinos knots with Δ-unknotting number one and provide examples admitting distinct Δ-moves, each of which deforms the knot into the trivial knot.

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Cite

BibTeXRIS
BibTeX
@misc{nakamura2026montesinos,
  title = {{Montesinos Knots with Delta-Unknotting Number One}},
  author = {Kazumichi Nakamura},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39565},
  eprint = {2609.39565},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39565},
}
RIS
TY  - UNPB
TI  - Montesinos Knots with Delta-Unknotting Number One
AU  - Kazumichi Nakamura
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.39565
UR  - https://arxiv.org/abs/2609.39565
AB  - The Δ-unknotting number for a knot is defined as the minimum number of Δ-moves needed to deform the knot into the trivial knot. In this paper, we discuss Montesinos knots whose Δ-unknotting number is equal to one. We propose a conjectural characterization of Montesinos knots with Δ-unknotting number one and provide examples admitting distinct Δ-moves, each of which deforms the knot into the trivial knot.
ER  -