Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Classification of Planar Contact Structures   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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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: stat
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex