Contact structures and reducible surgeries

Tye Lidman; Steven Sivek

doi:10.1112/s0010437x15007599

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arXiv · 1410.0303

Contact structures and reducible surgeries

Tye Lidman·Steven Sivek

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Abstract

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.

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Tye Lidman, Steven Sivek. 2014-10-01. Contact structures and reducible surgeries. https://doi.org/10.1112/s0010437x15007599

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