Journal of Symplectic Geometry

Volume 17 (2019)

Number 4

Contact surgeries on Legendrian figure-eight knots

Pages: 1061 – 1078

DOI: https://dx.doi.org/10.4310/JSG.2019.v17.n4.a4

Author

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

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.

Full Text (PDF format)

Received 14 November 2016

Accepted 18 August 2018

Published 24 October 2019