Quasi right-veering braids and non-loose links

2016/01/26 by Tetsuya Ito, Ito, Tetsuya, Keiko Kawamuro +1
Mathematics · #57M10 #57M12 #57M50 #57R17 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1601.07084

openalex publication_date 2016/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

Citations

• Essential open book foliation and fractional Dehn twist coefficient
• The defect of Bennequin-Eliashberg inequality and Bennequin surfaces

Related

• A Transverse Braiding Theorem with Rational Open Book Decomposition
• On the fractional Dehn twist coefficients of branched coverings
• Fibered Transverse Knots and the Bennequin Bound
• On the transverse invariant and braid dynamics
• Transverse links, open books and overtwisted manifolds