Geometry & Topology

Open book foliation

Tetsuya Ito and Keiko Kawamuro

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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.

Article information

Geom. Topol., Volume 18, Number 3 (2014), 1581-1634.

Received: 25 January 2013
Revised: 3 September 2013
Accepted: 19 October 2013
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57M50: Geometric structures on low-dimensional manifolds 57R17: Symplectic and contact topology 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx]

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


Ito, Tetsuya; Kawamuro, Keiko. Open book foliation. Geom. Topol. 18 (2014), no. 3, 1581--1634. doi:10.2140/gt.2014.18.1581.

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