Open book foliation

Ito, Tetsuya; Kawamuro, Keiko

doi:10.2140/gt.2014.18.1581

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Open book foliation

Tetsuya Ito and Keiko Kawamuro

Geometry & Topology 18 (2014) 1581–1634

DOI: 10.2140/gt.2014.18.1581

Abstract

We study open book foliations on surfaces in $3$ –manifolds and give applications to contact geometry of dimension $3$ . We prove a braid-theoretic formula for the self-linking number of transverse links, which reveals an unexpected connection with to the Johnson–Morita homomorphism in mapping class group theory. We also give an alternative combinatorial proof of the Bennequin–Eliashberg inequality.

Keywords

open book decomposition, contact structure, self-linking number, Johnson–Morita homomorphism

Mathematical Subject Classification 2010

Primary: 57M27

Secondary: 57M50, 57R17, 53D35

References

Publication

Received: 25 January 2013

Revised: 3 September 2013

Accepted: 19 October 2013

Published: 7 July 2014

Proposed: Shigeyuki Morita

Seconded: Yasha Eliashberg, Walter Neumann

Authors

Tetsuya Ito
Research Institute for Mathematical Sciences Kyoto University Sakyo-ku Kyoto 606-8502 Japan
http://kurims.kyoto-u.ac.jp/~tetitoh/
Keiko Kawamuro
Department of Mathematics The University of Iowa 14 McLean Hall Iowa City, IA 52242 USA

Volume 18, issue 3 (2014)