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

By John A. Baldwin, D. Vela-Vick, Vera Vértesi. 2011

49 citations recorded by the source corpus.

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. 57M27; 57R58

Subfields: Geometry and Topology, Neurology

View Paper: https://www.semanticscholar.org/paper/4848a2c8fdfb52917a196354f4fbc2c3ba60b2eb

Citations in the corpus

• AN INTRODUCTION TO KNOT FLOER HOMOLOGY (2014, unknown): “Knot Floer homology has further applications to contact geometry, as it allows the construction of invariants for Legendrian and transverse knots in S 3 ; see [OST08, NOT08, LOSS09, BVVV13].”
• Grid Homology for Knots and Links (2015, unknown): “Legendrian and transverse invariants in an arbitrary oriented, contact three-manifold were defined in [126]; and they were shown to generalize the grid invariants studied here, in work of Baldwin, Vela-Vick, and Vértesi [7].”