Translator Disclaimer
2018 Notes on open book decompositions for Engel structures
Vincent Colin, Francisco Presas, Thomas Vogel
Algebr. Geom. Topol. 18(7): 4275-4303 (2018). DOI: 10.2140/agt.2018.18.4275

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.

Citation

Download Citation

Vincent Colin. Francisco Presas. Thomas Vogel. "Notes on open book decompositions for Engel structures." Algebr. Geom. Topol. 18 (7) 4275 - 4303, 2018. https://doi.org/10.2140/agt.2018.18.4275

Information

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

zbMATH: 07006391
MathSciNet: MR3892245
Digital Object Identifier: 10.2140/agt.2018.18.4275

Subjects:
Primary: 58A30

Rights: Copyright © 2018 Mathematical Sciences Publishers

JOURNAL ARTICLE
29 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.18 • No. 7 • 2018
MSP
Back to Top