On the Classification of Planar Contact Structures

Details On the Classification of Planar Contact Structures On the Classification of Planar Contact Structures

2010-08-05

arxiv.org/abs/1008.1102v2

Mathematics

Geometric Topology

10 pages, 10 figures

Scientific paper

In this paper, we focus on contact structures supported by planar open book decompositions. We study right-veering diffeomorphisms to keep track of overtwistedness property of contact structures under some monodromy changes. As an application we give infinitely many examples of overtwisted contact structures supported by open books whose pages are the four-punctured sphere, and also we prove that a certain family is holomorphically fillable using lantern relation.

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