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2018 Braid monodromy, orderings and transverse invariants
Olga Plamenevskaya
Algebr. Geom. Topol. 18(6): 3691-3718 (2018). DOI: 10.2140/agt.2018.18.3691

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: θ̂0 if and only if the braid is right-veering.)

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Olga Plamenevskaya. "Braid monodromy, orderings and transverse invariants." Algebr. Geom. Topol. 18 (6) 3691 - 3718, 2018. https://doi.org/10.2140/agt.2018.18.3691

Information

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

zbMATH: 06990075
MathSciNet: MR3868232
Digital Object Identifier: 10.2140/agt.2018.18.3691

Subjects:
Primary: 57M27, 57R17, 57R58

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 6 • 2018
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