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arXiv · 1802.07639

Notes On Open Book Decompositions For Engel Structures

Vincent Colin·Francisco Presas·Thomas Vogel
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Abstract

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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Vincent Colin, Francisco Presas, Thomas Vogel. 2018-02-21. Notes On Open Book Decompositions For Engel Structures. https://doi.org/10.2140/agt.2018.18.4275

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