Scholarlink

Yasutaka Nakanishi formulated the following puzzling conjecture in 1981: every link is 3-move equivalent to a trivial link. While the conjecture was proved for several specific cases, it remained an open question for over twenty years. In 2002, Mieczysław Da¸bkowski and the last author showed that it does not hold in general. In this article, we outline the method of proving the Montesinos-Nakanishi 3-move conjecture for links with up to 19 crossings and, with the exception of six pairwise non-isotopic links including Chen’s link and its mirror image, for links with 20 crossings. Our work completely classifies links up 20 crossings modulo 3-moves.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Remarks on the Montesinos-Nakanishi 3-move conjecture

  • 章节

  • 发表日期：

    2026年

查看全文
  • Rhea Palak Bakshi,
  • Benjamin A. Burton,
  • Huizheng Guo,
  • Dionne Ibarra,
  • Gabriel Montoya-Vega,
  • Sujoy Mukherjee,
  • Józef H. Przytycki

摘要

Yasutaka Nakanishi formulated the following puzzling conjecture in 1981: every link is 3-move equivalent to a trivial link. While the conjecture was proved for several specific cases, it remained an open question for over twenty years. In 2002, Mieczysław Da¸bkowski and the last author showed that it does not hold in general. In this article, we outline the method of proving the Montesinos-Nakanishi 3-move conjecture for links with up to 19 crossings and, with the exception of six pairwise non-isotopic links including Chen’s link and its mirror image, for links with 20 crossings. Our work completely classifies links up 20 crossings modulo 3-moves.