Transverse invariants and right-veering
Abstract
A closed braid naturally gives rise to a transverse link in the standard contact 3-space. We study the effect of the dynamical properties of the braid monodromy, such as right-veering, on the contact-topological properties of the transverse link and its transverse invariants in knot Floer and Khovanov homologies. In particular, we show that a 3-braid is right-veering if and only if the (hat-version of) the Heegaard Floer transverse invariant is non-zero. For higher-index braids, we show that this invariant is non-zero whenever the braid monodromy has the fractional Dehn twist coefficient C>1. These results clarify the qualitative meaning of the transverse invariants; our proofs use grid diagrams and the structure of Dehornoy's braid ordering.
Cite
@article{arxiv.1509.01732,
title = {Transverse invariants and right-veering},
author = {Olga Plamenevskaya},
journal= {arXiv preprint arXiv:1509.01732},
year = {2018}
}