Journal of Differential Geometry

Cabling, contact structures and mapping class monoids

Kenneth L. Baker, John B. Etnyre, and Jeremy Van Horn-Morris

Full-text: Open access

Abstract

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.

Article information

Source
J. Differential Geom., Volume 90, Number 1 (2012), 1-80.

Dates
First available in Project Euclid: 23 April 2012

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1335209489

Digital Object Identifier
doi:10.4310/jdg/1335209489

Mathematical Reviews number (MathSciNet)
MR2891477

Zentralblatt MATH identifier
1252.53089

Citation

Baker, Kenneth L.; Etnyre, John B.; Van Horn-Morris, Jeremy. Cabling, contact structures and mapping class monoids. J. Differential Geom. 90 (2012), no. 1, 1--80. doi:10.4310/jdg/1335209489. https://projecteuclid.org/euclid.jdg/1335209489


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