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

John A Baldwin, David Shea Vela-Vick and Vera Vértesi

Geometry & Topology 17 (2013) 925–974

Using the grid diagram formulation of knot Floer homology, Ozsváth, Szabó and Thurston defined an invariant of transverse knots in the tight contact 3–sphere. Shortly afterwards, Lisca, Ozsváth, Stipsicz and Szabó 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.

Legendrian knots, transverse knots, Heegaard Floer homology
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57R58
Received: 27 December 2011
Revised: 18 December 2012
Accepted: 2 January 2013
Published: 30 April 2013
Proposed: Peter Ozsváth
Seconded: Yasha Eliashberg, Peter Teichner
John A Baldwin
Department of Mathematics
Boston College
Carney Hall, Room 301
Boston College
Chestnut Hill, MA 02467
David Shea Vela-Vick
Department of Mathematics
Louisiana State University
Lockett Hall
Baton Rouge, LA 70803
Vera Vértesi
Laboratorie de Mathématiques Jean Leray
UMR6629 du CNRS
Université de Nantes
2 rue de la Houssiniére
F-44322 Nantes