Transverse knots and Khovanov homology

We define an invariant of transverse links in $(S^3, \xi_{std})$ 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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Published 1 January 2006