Can Dehn surgery yield three connected summands?

James Howie

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arXiv · 0908.2697

Can Dehn surgery yield three connected summands?

James Howie

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Abstract

A consequence of the Cabling Conjecture of Gonzalez-Acuña 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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James Howie. 2009-08-19. Can Dehn surgery yield three connected summands?. https://arxiv.org/abs/0908.2697

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