Groups, Geometry, and Dynamics

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Volume 4, Issue 4, 2010, pp. 785–797
DOI: 10.4171/GGD/106

Published online: 2010-10-15

Can Dehn surgery yield three connected summands?

James Howie[1]

(1) Heriot-Watt University, Edinburgh, UK

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.

Keywords: Dehn surgery, cabling conjecture

Howie James: Can Dehn surgery yield three connected summands?. Groups Geom. Dyn. 4 (2010), 785-797. doi: 10.4171/GGD/106