Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Notes On Open Book Decompositions For Engel Structures   We relate open book decompositions of a 4-manifold M with its Engel
structures. Our main result is, given an open book decomposition of M whose
binding is a collection of 2-tori and whose monodromy preserves a framing of a
page, the construction of an En-gel structure whose isotropic foliation is
transverse to the interior of the pages and tangent to the binding. In
particular the pages are contact man-ifolds and the monodromy is a
contactomorphism. As a consequence, on a parallelizable closed 4-manifold,
every open book with toric binding carries in the previous sense an Engel
structure. Moreover, we show that amongst the supported Engel structures we
construct, there is a class of loose Engel structures.

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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: cond-mat