## Geometry & Topology

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

#### Abstract

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

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

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

https://projecteuclid.org/euclid.gt/1513732570

Digital Object Identifier
doi:10.2140/gt.2013.17.925

Mathematical Reviews number (MathSciNet)
MR3070518

Zentralblatt MATH identifier
1285.57005

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

#### Citation

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. https://projecteuclid.org/euclid.gt/1513732570

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