Algebraic & Geometric Topology

Quasi-right-veering braids and nonloose links

Tetsuya Ito and Keiko Kawamuro

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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 nonloose 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.

Article information

Algebr. Geom. Topol., Volume 19, Number 6 (2019), 2989-3032.

Received: 15 May 2018
Revised: 10 December 2018
Accepted: 30 January 2019
First available in Project Euclid: 29 October 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 57M27: Invariants of knots and 3-manifolds

quasi-right-veering loose transverse knots


Ito, Tetsuya; Kawamuro, Keiko. Quasi-right-veering braids and nonloose links. Algebr. Geom. Topol. 19 (2019), no. 6, 2989--3032. doi:10.2140/agt.2019.19.2989.

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