A slope p{q is said to be characterizing for a knot K if the homeomorphism type of the p{q-Dehn surgery along K determines the knot up to isotopy.Extending previous work of Lackenby and McCoy on hyperbolic and torus knots respectively, we study satellite knots to show that for a knot K, any slope p{q is characterizing provided |q| is sufficiently large.In particular, we establish that every non-integral slope is characterizing for a composite knot.Our approach consists of a detailed examination of the JSJ decomposition of a surgery along a knot, combined with results from other authors giving constraints on surgery slopes that yield manifolds containing certain surfaces.
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Patricia Sorya (2024) studied this question.
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