{"id":"openai-math/Purely-Cosmetic-Surgery-on-Knots-in-the-Three-Sphere","pdf":"https://github.com/openai/math/blob/main/preprints/Purely-Cosmetic-Surgery-on-Knots-in-the-Three-Sphere-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Purely-Cosmetic-Surgery-on-Knots-in-the-Three-Sphere-September-23-2026","tags":["knot-theory","dehn-surgery","low-dimensional-topology","3-manifolds"],"score":0,"title":"Purely cosmetic surgery on knots in the three-sphere","domain":"Topology","family":"306","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.GT","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"The purely cosmetic surgery conjecture"}