We introduce a notion of quasi-right-veering for closed braids, which plays an analogous role to right-veering for open books. We show that a transverse link in a contact –manifold is nonloose if and only if every braid representative of with respect to every open book decomposition that supports is quasi-right-veering. We also show that several definitions of right-veering closed braids are equivalent.
"Quasi-right-veering braids and nonloose links." Algebr. Geom. Topol. 19 (6) 2989 - 3032, 2019. https://doi.org/10.2140/agt.2019.19.2989