Open book foliation

Tetsuya Ito; Keiko Kawamuro

doi:10.2140/gt.2014.18.1581

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Home > Journals > Geom. Topol. > Volume 18 > Issue 3 > Article

2014 Open book foliation

Tetsuya Ito, Keiko Kawamuro

Geom. Topol. 18(3): 1581-1634 (2014). DOI: 10.2140/gt.2014.18.1581

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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.