On the equivalence of Legendrian and transverse invariants in knot Floer homology

Details On the equivalence of Legendrian and transverse invariants in knot Floer homology On the equivalence of Legendrian and transverse invariants in knot Floer homology

2011-12-27

arxiv.org/abs/1112.5970v1

Mathematics

Symplectic Geometry

41 pages, 29 figures

Scientific paper

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. We prove this fact by defining yet another invariant of transverse knots, showing that this third invariant agrees with the two mentioned above.

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