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Cabling, contact structures and mapping class monoids

Kenneth L. Baker University of Miami John B. Etnyre School of Mathematics Jeremy Van Horn-Morris American Institute of Mathematics

Differential Geometry mathscidoc:1609.10247

Journal of Differential Geometry, 90, (1), 1-80, 2012
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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@inproceedings{kenneth2012cabling,,
  title={CABLING, CONTACT STRUCTURES AND MAPPING CLASS MONOIDS},
  author={Kenneth L. Baker, John B. Etnyre, and Jeremy Van Horn-Morris},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913211714318952908},
  booktitle={Journal of Differential Geometry},
  volume={90},
  number={1},
  pages={1-80},
  year={2012},
}
Kenneth L. Baker, John B. Etnyre, and Jeremy Van Horn-Morris. CABLING, CONTACT STRUCTURES AND MAPPING CLASS MONOIDS. 2012. Vol. 90. In Journal of Differential Geometry. pp.1-80. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913211714318952908.
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