Rasmussen invariant, Slice-Bennequin inequality, and sliceness of knots
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.
Keywords
Cite
@article{arxiv.math/0411643,
title = {Rasmussen invariant, Slice-Bennequin inequality, and sliceness of knots},
author = {Alexander N. Shumakovitch},
journal= {arXiv preprint arXiv:math/0411643},
year = {2018}
}
Comments
9 pages, 4 tables and 1 figure. Updated to match the published version: Corollary 1.D is made more general to work with links instead of knots, a comment on the relation between the total rank of the reduced Khovanov homology and computations of the Rasmussen invariant is added. Journal reference is added and references are updated