A characterization of quasipositive two-bridge knots. (English) Zbl 07844493
Summary: 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 Appendix A, by Stepan Orevkov.
MSC:
| 57K10 | Knot theory |
| 57K33 | Contact structures in 3 dimensions |
| 57K43 | Symplectic structures in 4 dimensions |
Keywords:
two-bridge knot; quasi positive knot; strongly quasi positive knot; slice knot; alternating link; Montesinos link; contact structure; symplectic structureReferences:
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