Invariants for transverse knots in Heegaard Floer homology

Using the grid diagram formulation of knot Floer homology, Ozsvath, Szabo and Thurston defined an invariant of transverse knots in the tight contact 3-sphere. Shortly afterwards, Lisca, Ozsvath, Stipsicz and Szabo defined an invariant of transverse knots in arbitrary contact 3-manifolds using open book decompositions. It has been conjectured that these invariants agree where they are both defined. In this talk, I prove this fact by defining yet another invariant of transverse knots, showing that this third invariant agrees with the two mentioned above.

This is a joint work with John A. Baldwin and David Shea Vela-Vick.