Algebraic & Geometric Topology

Notes on open book decompositions for Engel structures

Vincent Colin, Francisco Presas, and 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 Engel structure whose isotropic foliation is transverse to the interior of the pages and tangent to the binding.

In particular, the pages are contact manifolds and the monodromy is a compactly supported 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 among the supported Engel structures we construct, there are loose Engel structures.

Article information

Source
Algebr. Geom. Topol., Volume 18, Number 7 (2018), 4275-4303.

Dates
Received: 21 February 2018
Revised: 12 April 2018
Accepted: 21 June 2018
First available in Project Euclid: 18 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.agt/1545102071

Digital Object Identifier
doi:10.2140/agt.2018.18.4275

Mathematical Reviews number (MathSciNet)
MR3892245

Zentralblatt MATH identifier
07006391

Subjects
Primary: 58A30: Vector distributions (subbundles of the tangent bundles)

Keywords
open book decomposition Engel structures contact structure

Citation

Colin, Vincent; Presas, Francisco; Vogel, Thomas. Notes on open book decompositions for Engel structures. Algebr. Geom. Topol. 18 (2018), no. 7, 4275--4303. doi:10.2140/agt.2018.18.4275. https://projecteuclid.org/euclid.agt/1545102071


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