Knots admitting purely cosmetic surgeries are prime (Q2104992)

In this paper, the author proves that composite knots satisfy the Cosmetic Surgery Conjecture, i.e., different Dehn surgeries along a prime knot in the 3-sphere yield two 3-manifolds which can't be orientation-preserving homeomorphic. The author shows this result by studying the JSJ-structures, a method which was applied to cable knots before. The proof can be reduced to analyzing cases of some special surgery slopes, especially, integers and half integers.