Open Access
January 2012 Cabling, contact structures and mapping class monoids
Kenneth L. Baker, John B. Etnyre, Jeremy Van Horn-Morris
J. Differential Geom. 90(1): 1-80 (January 2012). DOI: 10.4310/jdg/1335209489


In this paper we discuss the change in contact structures as their supporting open book decompositions have their binding components cabled. To facilitate this and applications we define the notion of a rational open book decomposition that generalizes the standard notion of open book decomposition and allows one to more easily study surgeries on transverse knots. As a corollary to our investigation we are able to show there are Stein fillable contact structures supported by open books whose monodromies cannot be written as a product of positive Dehn twists. We also exhibit several monoids in the mapping class group of a surface that have contact geometric significance.


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Kenneth L. Baker. John B. Etnyre. Jeremy Van Horn-Morris. "Cabling, contact structures and mapping class monoids." J. Differential Geom. 90 (1) 1 - 80, January 2012.


Published: January 2012
First available in Project Euclid: 23 April 2012

zbMATH: 1252.53089
MathSciNet: MR2891477
Digital Object Identifier: 10.4310/jdg/1335209489

Rights: Copyright © 2012 Lehigh University

Vol.90 • No. 1 • January 2012
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