#### Volume 18, issue 6 (2018)

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Braid monodromy, orderings and transverse invariants

### Olga Plamenevskaya

Algebraic & Geometric Topology 18 (2018) 3691–3718
##### Abstract

A closed braid $\beta$ 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 $\beta$, 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 $\stackrel{̂}{\theta }\left(K\right)\in \stackrel{̂}{HFK}\left(m\left(K\right)\right)$ is nonzero whenever $\beta$ has fractional Dehn twist coefficient $C>1$. (For a $3$–braid, we get a sharp result: $\stackrel{̂}{\theta }\ne 0$ if and only if the braid is right-veering.)

##### Keywords
Heegaard Floer transverse invariants, right-veering, fractional Dehn twist coefficient, grid diagrams
##### Mathematical Subject Classification 2010
Primary: 57M27, 57R17, 57R58
##### Publication
Revised: 8 June 2018
Accepted: 18 June 2018
Published: 18 October 2018
##### Authors
 Olga Plamenevskaya Department of Mathematics Stony Brook University Stony Brook, NY United States