Exceptional cosmetic surgeries on S3

This paper concerns the truly cosmetic surgery conjecture. We prove that the slope of an exceptional truly cosmetic surgery on a hyperbolic knot in S3S3 must be ±1 and the surgery must be toroidal but not Seifert fibred. As a consequence we show that there are no exceptional truly cosmetic surgeries on certain types of hyperbolic knots in S3S3. We also give some properties of Heegaard Floer correction terms and torsion invariants for exceptional cosmetic surgeries on S3S3.