Transverse invariants in filtrations of Khovanov homology

Transverse invariants in filtrations of Khovanov homology

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Alan Diaz, Georgia Tech
Fine Hall 314

In 2005, O. Plamenevskaya used Khovanov homology to define an invariant \psi of transverse knots T in R^3. Since then, related invariants have been defined using spectral sequences that start at Khovanov homology. On a similar note, Baldwin and Plamenevskaya related \psi to the Heegaard Floer contact invariant of the double branched cover of T using the Ozsvath-Szabo spectral sequence. However, it has been unknown whether \psi was a strictly stronger invariant of T than the classical self-linking number. I will give a proof that \psi is in fact determined by self-linking, and explain how a similar argument shows that the contact invariant of the double branched cover is also determined by self-linking. If time permits I will discuss some of the other transverse invariants, and the 2012 theorem of Dynnikov and Prasolov that forms a key part of the proof.