Geometry & Topology
- Geom. Topol.
- Volume 18, Number 3 (2014), 1581-1634.
Open book foliation
Tetsuya Ito and Keiko Kawamuro
Full-text: Open access
Abstract
We study open book foliations on surfaces in –manifolds and give applications to contact geometry of dimension . 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
Received: 25 January 2013
Revised: 3 September 2013
Accepted: 19 October 2013
First available in Project Euclid: 20 December 2017
Permanent link to this document
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
Subjects
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]
Keywords
open book decomposition contact structure self-linking number Johnson–Morita homomorphism
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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