Open Book Foliations
Geometric Topology
2014-11-11 v3 Symplectic Geometry
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 of the self-linking number of transverse links, which reveals an unexpected link to the Johnson-Morita homomorphism in mapping class group theory. We also give an alternative combinatorial proof to the Bennequin-Eliashberg inequality.
Keywords
Cite
@article{arxiv.1112.5874,
title = {Open Book Foliations},
author = {Tetsuya Ito and Keiko Kawamuro},
journal= {arXiv preprint arXiv:1112.5874},
year = {2014}
}
Comments
47 pages, 34 figures, accepted by Geometry and Topology. Title, abstract, expositions have been changed. The last section of Version 1 is now included in another paper "Visualizing overtwisted discs in open books" (arXiv:1310.6404)