Transverse knots and Khovanov homology
Geometric Topology
2007-05-23 v1 Symplectic Geometry
Abstract
We define an invariant of transverse links in the standard contact 3-sphere as a distinguished element of the Khovanov homology of the link. The quantum grading of this invariant is the self-linking number of the link. For knots, this gives a bound on the self-linking number in terms of Rasmussen's invariant s(K). We prove that our invariant vanishes for transverse knot stabilizations, and that it is non-zero for quasipositive braids. We also discuss a connection to Heegaard Floer invariants.
Keywords
Cite
@article{arxiv.math/0412184,
title = {Transverse knots and Khovanov homology},
author = {Olga Plamenevskaya},
journal= {arXiv preprint arXiv:math/0412184},
year = {2007}
}