Chirally cosmetic surgery conjecture for chiral knots

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A knot KK is chiral if it is not equivalent to its mirror image, and T(2,n)T(2,n) denotes the (2,n)(2,n) torus knot. Chirally cosmetic surgery conjecture. If KK is a chiral knot that is not a torus knot T(2,n)T(2,n), then KK 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.

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