Contact structures and reducible surgeries

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.

33 pages

References in corpus (1)

• Knot Floer homology detects fibred knots

Cited by in corpus (5)

• Shake slice and shake concordant knots
• On the equivalence of contact invariants in sutured Floer homology theories
• Augmentations and Rulings of Legendrian Links in ${\#}^k(S^1\times S^2)$
• Legendrian Large Cables And New Phenomenon For Non-Uniformly Thick Knots
• Maximal Thurston-Bennequin number and reducible Legendrian surgery