Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 18, Number 7 (2018), 4275-4303.
Notes on open book decompositions for Engel structures
We relate open book decompositions of a –manifold with its Engel structures. Our main result is, given an open book decomposition of whose binding is a collection of –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 –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.
Algebr. Geom. Topol., Volume 18, Number 7 (2018), 4275-4303.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 58A30: Vector distributions (subbundles of the tangent bundles)
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