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July 2015 L-space surgeries, genus bounds, and the cabling conjecture
Joshua Evan Greene
J. Differential Geom. 100(3): 491-506 (July 2015). DOI: 10.4310/jdg/1432842362

Abstract

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.

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Joshua Evan Greene. "L-space surgeries, genus bounds, and the cabling conjecture." J. Differential Geom. 100 (3) 491 - 506, July 2015. https://doi.org/10.4310/jdg/1432842362

Information

Published: July 2015
First available in Project Euclid: 28 May 2015

zbMATH: 1325.57016
MathSciNet: MR3352796
Digital Object Identifier: 10.4310/jdg/1432842362

Rights: Copyright © 2015 Lehigh University

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Vol.100 • No. 3 • July 2015
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