Paper published by Geometry and Topology

The following paper has been published:

Geometry and Topology, Volume 9 (2005) Paper no. 50, pages 2193--2226

URL:
http://www.maths.warwick.ac.uk/gt/GTVol9/paper50.abs.html

DOI: 10.2140/gt.2005.9.2193

Title:
Constructions controlees de champs de Reeb et applications

Author(s):
Vincent Colin, Ko Honda

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 bdry 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 bdry V is irreducible and different from the 3-sphere.

Resume:

On construit, sur toute variete V de dimension trois orientable,
compacte, irreductible, bordee par des tores ou toroidale, une forme
de contact dont le champ de Reeb R est sans orbite periodique
contractible et tangent au bord. De plus, si le bord de V est non
vide, le champ R est transversal a un feuilletage tendu. En utilisant
des resultats de Hofer, Wysocki et Zehnder, on obtient sous certaines
conditions que la variete obtenue par obturation de Dehn le long du
bord de V est irreductible et differente de la sphere S^3.

AMS Classification Numbers. Primary: 53D35
Secondary: 53C15

Keywords:
Reeb vector field, contact structure, taut foliation

Received: 25 November 2004
Revised: 4 September 2005
Accepted: 26 November 2005
Published: 1 December 2005

Proposed: Yasha Eliashberg
Seconded: Tomasz Mrowka, Joan Birman

Author(s) address(es):
Universite de Nantes, UMR 6629 du CNRS, 44322 Nantes, France
and
University of Southern California, Los Angeles, CA 90089, USA
Email: Vincent.Colin@xxxxxxxxxxxxxxxxxxx, khonda@xxxxxxxxxxxx
URL: http://rcf.usc.edu/~khonda

.