Transverse knots and Khovanov homology

Olga Plamenevskaya

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Transverse knots and Khovanov homology

Olga Plamenevskaya

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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.

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Olga Plamenevskaya. 2004-12-08. Transverse knots and Khovanov homology. https://arxiv.org/abs/math/0412184

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