Connected sums of knots do not admit purely cosmetic surgeries
arXiv:1909.05048
Abstract
Two Dehn surgeries on a knot are called purely cosmetic if their surgered manifolds are homeomorphic as oriented manifolds. Gordon conjectured that non-trivial knots in do not admit purely cosmetic surgeries. In this article, we confirm this conjecture for connected sums of knots by analysing the JSJ-structures.
11 pages, 5 figures