Journal of Differential Geometry
- J. Differential Geom.
- Volume 90, Number 1 (2012), 1-80.
Cabling, contact structures and mapping class monoids
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.
J. Differential Geom., Volume 90, Number 1 (2012), 1-80.
First available in Project Euclid: 23 April 2012
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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