A characterization of quasipositive two-bridge knots

Abstract

We prove a simple necessary and sufficient condition for a two-bridge knot K(p,q) to be quasipositive, based on the continued fraction expansion of p/q. As an application, coupled with some classification results in contact and symplectic topology, we give a new proof of the fact that smoothly slice two-bridge knots are non-quasipositive. Another proof of this fact using methods within the scope of knot theory is presented in the Appendix.

arXiv commentIncludes an Appendix by Stepan Orevkov. This is the final version that will appear in the International Journal of Mathematics