Cabling, contact structures and mapping class monoids

Details Cabling, contact structures and mapping class monoids Cabling, contact structures and mapping class monoids

2010-05-12

arxiv.org/abs/1005.1978v2

Mathematics

Symplectic Geometry

62 pages, 32 figures. Significant expansion of exposition and more details on some arguments

Scientific paper

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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