Algebraic & Geometric Topology

Braid monodromy, orderings and transverse invariants

Olga Plamenevskaya

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A closed braid β naturally gives rise to a transverse link K in the standard contact 3–space. We study the effect of the dynamical properties of the monodromy of β, such as right-veering, on the contact-topological properties of K and the values of transverse invariants in Heegaard Floer and Khovanov homologies. Using grid diagrams and the structure of Dehornoy’s braid ordering, we show that θ̂(K)HFK̂(m(K)) is nonzero whenever β has fractional Dehn twist coefficient C>1. (For a 3–braid, we get a sharp result: θ̂0 if and only if the braid is right-veering.)

Article information

Algebr. Geom. Topol., Volume 18, Number 6 (2018), 3691-3718.

Received: 21 March 2018
Revised: 8 June 2018
Accepted: 18 June 2018
First available in Project Euclid: 27 October 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M27: Invariants of knots and 3-manifolds 57R17: Symplectic and contact topology 57R58: Floer homology

Heegaard Floer transverse invariants right-veering fractional Dehn twist coefficient grid diagrams


Plamenevskaya, Olga. Braid monodromy, orderings and transverse invariants. Algebr. Geom. Topol. 18 (2018), no. 6, 3691--3718. doi:10.2140/agt.2018.18.3691.

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