#### Volume 18, issue 3 (2014)

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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