Volume 18, issue 3 (2014)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Open book foliation

Tetsuya Ito and Keiko Kawamuro

Geometry & Topology 18 (2014) 1581–1634
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