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A characterization of quasipositive two-bridge knots

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Orevkov, Stepan

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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.

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World Scientific Publ Co Pte Ltd

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Mathematics

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International Journal of Mathematics

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10.1142/S0129167X24500150

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