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

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

2004-11-29

arxiv.org/abs/math/0411643v1

Mathematics

Geometric Topology

7 pages, 4 tables, and 1 figure

Scientific paper

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 were to the best of our knowledge unknown before.

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