Geometry & Topology

Constructions controlees de champs de Reeb et applications

Vincent Colin and Ko Honda

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Abstract

On every compact, orientable, irreducible 3–manifold V which is toroidal or has torus boundary components we construct a contact 1–form whose Reeb vector field R does not have any contractible periodic orbits and is tangent to the boundary. Moreover, if V is nonempty, then the Reeb vector field R is transverse to a taut foliation. By appealing to results of Hofer, Wysocki, and Zehnder, we show that, under certain conditions, the 3–manifold obtained by Dehn filling along V is irreducible and different from the 3–sphere.

R é sum é

On construit, sur toute variété V de dimension trois orientable, compacte, irréductible, bordée par des tores ou toroïdale, une forme de contact dont le champ de Reeb R est sans orbite périodique contractible et tangent au bord. De plus, si V est non vide, le champ R est transversal à un feuilletage tendu. En utilisant des résultats de Hofer, Wysocki et Zehnder, on obtient sous certaines conditions que la variété obtenue par obturation de Dehn le long du bord de V est irréductible et différente de la sphère S3.

Article information

Source
Geom. Topol., Volume 9, Number 4 (2005), 2193-2226.

Dates
Received: 25 November 2004
Revised: 4 September 2005
Accepted: 26 November 2005
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513799678

Digital Object Identifier
doi:10.2140/gt.2005.9.2193

Mathematical Reviews number (MathSciNet)
MR2209370

Zentralblatt MATH identifier
1091.53057

Subjects
Primary: 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx]
Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)

Keywords
Reeb vector field contact structure taut foliation

Citation

Colin, Vincent; Honda, Ko. Constructions controlees de champs de Reeb et applications. Geom. Topol. 9 (2005), no. 4, 2193--2226. doi:10.2140/gt.2005.9.2193. https://projecteuclid.org/euclid.gt/1513799678


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