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Rasmussen invariant, Slice-Bennequin inequality, and sliceness of knots

Alexander N. Shumakovitch
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Abstract

We use recently introduced Rasmussen invariant to find knots that are topologically locally-flatly slice but not smoothly slice. We note that this invariant can be used to give a combinatorial proof of the slice-Bennequin inequality. Finally, we compute the Rasmussen invariant for quasipositive knots and show that most of our examples of non-slice knots are not quasipositive and, to the best of our knowledge, were previously unknown.

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Alexander N. Shumakovitch. 2004-11-29. Rasmussen invariant, Slice-Bennequin inequality, and sliceness of knots. https://arxiv.org/abs/math/0411643

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