L-space surgeries, genus bounds, and the cabling conjecture

We establish a tight inequality relating the knot genus g(K) and the surgery slope p under the assumption that p-framed Dehn surgery along K is an L-space that bounds a sharp 4-manifold. This inequality applies in particular when the surgered manifold is a lens space or a connected sum thereof. Comb...

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Bibliographic Details
Published in:Journal of differential geometry 2015-07, Vol.100 (no. 3), p.491-506
Main Author: Greene, Joshua Evan
Format: Article
Language:English
Online Access:Get full text
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Summary:We establish a tight inequality relating the knot genus g(K) and the surgery slope p under the assumption that p-framed Dehn surgery along K is an L-space that bounds a sharp 4-manifold. This inequality applies in particular when the surgered manifold is a lens space or a connected sum thereof. Combined with work of Gordon–Luecke, Hoffman, and Matignon–Sayari, it follows that if surgery along a knot produces a connected sum of lens spaces, then the knot is either a torus knot or a cable thereof, confirming the cabling conjecture in this case.
ISSN:1945-743X