Journal of Differential Geometry

Cabling, contact structures and mapping class monoids

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

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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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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.

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