Groups, Geometry, and Dynamics
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Published online: 2010-10-15
Can Dehn surgery yield three connected summands?James Howie (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