Families of cosmetic surgeries

Abstract

We construct infinite families of chirally cosmetic surgeries on chiral hyperbolic knots and purely cosmetic surgeries on hyperbolic manifolds with multiple cusps, disproving conjectures that these phenomena do not appear, including Problem 1.12(d) in the K3 problem list. We also give some hints regarding why chirally cosmetic surgeries appear to be more common than purely cosmetic surgeries on $1$-cusped manifolds.