Can Dehn surgery yield three connected summands?

A consequence of the Cabling Conjecture of Gonzalez-Acuña and Short is that Dehn surgeryon aknot in S³ cannot producea manifold with more than two connected summands. In the event that some Dehn surgery produces a manifold with three or more connected summands, then the surgery parameter is bounded in terms of the bridge number by a result of Sayari. Here this bound is sharpened, providing further evidence in favour of the Cabling Conjecture. © European Mathematical Society.