Mathematical Research Letters

Volume 13 (2006)

Number 4

Transverse knots and Khovanov homology

Pages: 571 – 586



Olga Plamenevskaya (Massachusetts Institute of Technology)


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.

Published 1 January 2006