Article contents
Contact structures and reducible surgeries
Published online by Cambridge University Press: 24 September 2015
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.
MSC classification
- Type
- Research Article
- Information
- Copyright
- © The Authors 2015
References
- 5
- Cited by