A consequence of the Cabling Conjecture of Gonzalez-Acuña 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.
Cite this article
James Howie, Can Dehn surgery yield three connected summands?. Groups Geom. Dyn. 4 (2010), no. 4, pp. 785–797DOI 10.4171/GGD/106