#### Volume 19, issue 6 (2019)

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Quasi-right-veering braids and nonloose links

### Tetsuya Ito and Keiko Kawamuro

Algebraic & Geometric Topology 19 (2019) 2989–3032
##### 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 $\left(M,\xi \right)$ is nonloose if and only if every braid representative of $K$ with respect to every open book decomposition that supports $\left(M,\xi \right)$ is quasi-right-veering. We also show that several definitions of right-veering closed braids are equivalent.

##### Keywords
quasi-right-veering, loose transverse knots
Primary: 57M50
Secondary: 57M27
##### Publication
Received: 15 May 2018
Revised: 10 December 2018
Accepted: 30 January 2019
Published: 20 October 2019
##### Authors
 Tetsuya Ito Department of Mathematics Kyoto University Kyoto Japan Keiko Kawamuro Department of Mathematics The University of Iowa Iowa City, IA United States