Heriot-Watt Mathematics Report Series
HWM09-7, 19 Aug 2009
Can Dehn surgery yield three connected summands?
J Howie
Abstract
A consequence of the Cabling Conjecture of Gonzalez-Acu\~{n}a and Short
is that Dehn surgery on a knot in $S^3$ 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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Full text: http://arxiv.org/abs/0908.2697
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