Journal of Symplectic Geometry

Volume 17 (2019)

Number 4

Contact surgeries on Legendrian figure-eight knots

Pages: 1061 – 1078



James Conway (Department of Mathematics, University of California at Berkeley)


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.

Received 14 November 2016

Accepted 18 August 2018

Published 24 October 2019