Quasi right-veering braids and non-loose links

Abstract

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 $K$ in a contact 3-manifold $(M,\xi )$ is non-loose if and only if every braid representative of $K$ with respect to every open book decomposition that supports $(M,\xi )$ is quasi-right-veering. We also show that several definitions of "right-veering" closed braids are equivalent.

28 pages, 10 figures

References in corpus (2)

• Transverse invariants and right-veering
• The defect of Bennequin-Eliashberg inequality and Bennequin surfaces

Cited by in corpus (2)

• On the fractional Dehn twist coefficients of branched coverings
• The defect of Bennequin-Eliashberg inequality and Bennequin surfaces