Chirally cosmetic surgery conjecture for chiral knots
A knot is chiral if it is not equivalent to its mirror image, and denotes the torus knot. Chirally cosmetic surgery conjecture. If is a chiral knot that is not a torus knot , then does not admit chirally cosmetic surgeries. The source notes known chirally cosmetic fillings on hyperbolic manifolds and states that its constructions give infinite families on chiral hyperbolic knots, thereby disproving this conjecture.
References
Primary source
Qiuyu Ren, “Families of cosmetic surgeries”, arXiv:2604.02672 (2026).
Additional references
4 papers in this index state this conjecture (2022–2026). The statement above is taken from the most recent of them; the others are arXiv:2311.02829, arXiv:2308.10126, arXiv:2209.10723.
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
No solutions have been posted yet.