Contact Surgeries on the Legendrian Figure-Eight Knot

preprint2016arXivOpen access

Abstract

We show that all positive contact surgeries on every Legendrian figure-eight knot in (S3,ξstd)(S^3, ξ_{\rm{std}}) result in an overtwisted contact structure. The proof uses convex surface theory and invariants from Heegaard Floer homology.

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