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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 (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.

Keywords
quasi-right-veering, loose transverse knots
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 57M27
References
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