Geometry & Topology

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

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

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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.

Article information

Geom. Topol., Volume 17, Number 2 (2013), 925-974.

Received: 27 December 2011
Revised: 18 December 2012
Accepted: 2 January 2013
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57R58: Floer homology

Legendrian knots transverse knots Heegaard Floer homology


Baldwin, John A; Vela-Vick, David; Vértesi, Vera. On the equivalence of Legendrian and transverse invariants in knot Floer homology. Geom. Topol. 17 (2013), no. 2, 925--974. doi:10.2140/gt.2013.17.925.

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