A characterization of quasipositive two-bridge knots

Abstract

We prove a simple necessary and sufficient condition for a two-bridge knot [Formula: see text] to be quasipositive, based on the continued fraction expansion of [Formula: see text]. 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 Appendix A, by Stepan Orevkov.