## Geometry & Topology

### Open book foliation

#### 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.

#### Article information

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

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

https://projecteuclid.org/euclid.gt/1513732802

Digital Object Identifier
doi:10.2140/gt.2014.18.1581

Mathematical Reviews number (MathSciNet)
MR3228459

Zentralblatt MATH identifier
1303.57012

#### Citation

Ito, Tetsuya; Kawamuro, Keiko. Open book foliation. Geom. Topol. 18 (2014), no. 3, 1581--1634. doi:10.2140/gt.2014.18.1581. https://projecteuclid.org/euclid.gt/1513732802

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