The Montesinos–Nakanishi 3-move conjecture
A 3-move is the local link move shown in the cited figure. A link is trivial if it is a disjoint union of unknotted, unlinked circles.
Montesinos–Nakanishi 3-move conjecture. Every link can be reduced to a trivial link by 3-moves.
This conjecture was formulated by Nakanishi in 1981 and disproved in 2002 by M. K. Dąbkowski and the author.
References
Primary source
Jozef H. Przytycki, “Path to homology of Yang-Baxter operators”, arXiv:2607.28626 (2026).
Additional references
6 papers in this index state this conjecture (2000–2026). The statement above is taken from the most recent of them; the others are arXiv:math/0606633, arXiv:math/0312527, arXiv:math/0205040, arXiv:math/0109029, arXiv:math/0010282.
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