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Constructions controlees de
champs de Reeb et applications
Vincent Colin and Ko Honda |
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Geometry & Topology 9 (2005) 2193–2226
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arXiv: math.GT/0411640 |
Abstract |
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On every compact, orientable, irreducible 3–manifold which is toroidal or has torus boundary components we construct a contact 1–form whose Reeb vector field does not have any contractible periodic orbits and is tangent to the boundary. Moreover, if is nonempty, then the Reeb vector field 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 is irreducible and different from the 3–sphere. Résumé On construit, sur toute variété de dimension trois orientable, compacte, irréductible, bordée par des tores ou toroïdale, une forme de contact dont le champ de Reeb est sans orbite périodique contractible et tangent au bord. De plus, si est non vide, le champ 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 est irréductible et différente de la sphère . |
Keywords
Reeb vector field, contact structure, taut foliation
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Mathematical Subject Classification 2000
Primary: 53D35
Secondary: 53C15
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References |
Forward citations |
Publication
Received: 25 November 2004
Revised: 4 September 2005
Accepted: 26 November 2005
Published: 1 December 2005
Proposed: Yasha Eliashberg
Seconded: Tomasz Mrowka, Joan Birman
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Authors |
| Vincent Colin | |
| Université de Nantes UMR 6629 du CNRS 44322 Nantes France |
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| Ko Honda | |
| University of Southern
California Los Angeles California 90089 USA |
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