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The purely cosmetic surgery conjecture
Distinct Dehn surgery slopes on a nontrivial smooth knot in S never produce orientation-preservingly homeomorphic manifolds, proving the purely cosmetic surgery conjecture. The statement includes the meridional slope.
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Purely cosmetic surgery on knots in the three-sphere
Sep 23, 2026·paper.pdf
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.