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Contact structures and reducible surgeries
Published online by Cambridge University Press: 24 September 2015
Abstract
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We apply results from both contact topology and exceptional surgery theory to study when Legendrian surgery on a knot yields a reducible manifold. As an application, we show that a reducible surgery on a non-cabled positive knot of genus 
$g$ must have slope 
$2g-1$, leading to a proof of the cabling conjecture for positive knots of genus 2. Our techniques also produce bounds on the maximum Thurston–Bennequin numbers of cables.
MSC classification
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