Can Dehn surgery yield three connected summands?
Abstract
A consequence of the Cabling Conjecture of Gonzalez-Acu\~na and Short is that Dehn surgery on a knot in S3 cannot produce a 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.
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