A characterization of quasipositive two-bridge knots

Burak Ozbagci

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arXiv · 2307.07179

A characterization of quasipositive two-bridge knots

Burak Ozbagci

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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.

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Burak Ozbagci. 2023-07-14. A characterization of quasipositive two-bridge knots. https://arxiv.org/abs/2307.07179

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