## Algebraic & Geometric Topology

### Braid monodromy, orderings and transverse invariants

Olga Plamenevskaya

#### Abstract

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: $θ̂≠0$ if and only if the braid is right-veering.)

#### Article information

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

Dates
Revised: 8 June 2018
Accepted: 18 June 2018
First available in Project Euclid: 27 October 2018

https://projecteuclid.org/euclid.agt/1540605654

Digital Object Identifier
doi:10.2140/agt.2018.18.3691

Mathematical Reviews number (MathSciNet)
MR3868232

Zentralblatt MATH identifier
06990075

#### Citation

Plamenevskaya, Olga. Braid monodromy, orderings and transverse invariants. Algebr. Geom. Topol. 18 (2018), no. 6, 3691--3718. doi:10.2140/agt.2018.18.3691. https://projecteuclid.org/euclid.agt/1540605654

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