The Weak Generalized Property R Conjecture
An R-link is a link such that 0-surgery on yields a connected sum of copies of . A 0-framed unlink is an unlink whose components all have framing zero, and a split collection of Hopf pairs is a collection of split Hopf-link pairs. The Weak Generalized Property R Conjecture. For every R-link , there is a 0-framed unlink and a split collection of Hopf pairs such that the split union is handleslide-equivalent to an unlink and a split collection of Hopf pairs.
This is a weaker variant of the Generalized Property R Conjecture. The source says that the GST links satisfy the weak conjecture, so this candidate is solved.
References
Primary source
Wenjie Diao, Haoqian Pan and Chunxing Yan, “Some experimental results on stable equivalence of GST Links for the Generalized Property R Conjecture”, arXiv:2604.17737 (2026).
Additional references
5 papers in this index state this conjecture (2009–2026). The statement above is taken from the most recent of them; the others are arXiv:2603.05664, arXiv:1507.06561, arXiv:1103.1601, arXiv:0908.2795.
Progress summary
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Solutions 0
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