Preprint in the OpenAI Math release
Purely cosmetic surgery on knots in the three-sphere
OpenAI
Abstract
We prove the purely cosmetic surgery conjecture for knots in the three-sphere. Distinct Dehn surgery slopes on a nontrivial smooth knot never give orientation-preservingly homeomorphic manifolds.
open until 1 Jan 2028
est. 50% chance this result is independently verified by the end of 2027.
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