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Braid monodromy, orderings and transverse invariants

Olga Plamenevskaya

Algebraic & Geometric Topology 18 (2018) 3691–3718
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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Keywords
Heegaard Floer transverse invariants, right-veering, fractional Dehn twist coefficient, grid diagrams
Mathematical Subject Classification 2010
Primary: 57M27, 57R17, 57R58
References
Publication
Received: 21 March 2018
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