Transverse knots and Khovanov homology

Details Transverse knots and Khovanov homology Transverse knots and Khovanov homology

2004-12-08

arxiv.org/abs/math/0412184v1

Mathematics

Geometric Topology

Scientific paper

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.

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