Contact Surgeries on the Legendrian Figure-Eight Knot

Abstract

We show that all positive contact surgeries on every Legendrian figure-eight knot in $(S^3,{\xi }_{\mathrm{std}})$ result in an overtwisted contact structure. The proof uses convex surface theory and invariants from Heegaard Floer homology.

12 pages, 9 figures

References in corpus (1)

• Lectures on Contact Geometry in Low-Dimensional Topology