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Notes on open book
decompositions for Engel structures
Vincent Colin, Francisco Presas and Thomas Vogel |
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Algebraic & Geometric Topology 18 (2018) 4275–4303
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Abstract |
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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. |
Keywords
open book decomposition, Engel structures, contact
structure
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Mathematical Subject Classification 2010
Primary: 58A30
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References |
Publication
Received: 21 February 2018
Revised: 12 April 2018
Accepted: 21 June 2018
Published: 11 December 2018
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Authors |
| Vincent Colin | |
| Laboratoire de Mathématiques Jean
Leray Université de Nantes Nantes France |
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| Francisco Presas | |
| Instituto de Ciencias
Matemáticas CSIC–UAM–UC3M–UCM Madrid Spain |
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| Thomas Vogel | |
| Mathematisches Institut der
Ludwig-Maximilians-Universität Universität München München Germany |
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