Quasi-right-veering braids and nonloose links

Ito, Tetsuya; Kawamuro, Keiko

doi:10.2140/agt.2019.19.2989

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Quasi-right-veering braids and nonloose links

Tetsuya Ito and Keiko Kawamuro

Algebraic & Geometric Topology 19 (2019) 2989–3032

DOI: 10.2140/agt.2019.19.2989

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

Volume 19, issue 6 (2019)