Volume 9, issue 1 (2005)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Homologie de contact des variétés toroïdales

Frédéric Bourgeois and Vincent Colin

Geometry & Topology 9 (2005) 299–313

arXiv: math.GT/0411577

Abstract

We show that contact homology distinguishes infinitely many tight contact structures on any orientable, toroidal, irreducible 3–manifold. As a consequence of the contact homology computations, on a very large class of toroidal manifolds, all known examples of universally tight contact structures with nonvanishing torsion satisfy the Weinstein conjecture.

Résumé

On montre que l’homologie de contact distingue une infinité de structures de contact tendues sur toute variété toroïdale irréductible et orientable de dimension trois. En conséquence des calculs d’homologie de contact, sur une très large classe de variétés toroïdales, tous les exemples de structures de contact universellement tendues de torsion non nulle connus vérifient la conjecture de Weinstein.

Keywords
Contact structures, Reeb fields, contact homology, toroidal manifolds, Weinstein conjecture
Mathematical Subject Classification 2000
Primary: 53D35
Secondary: 53C15
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Publication
Received: 25 November 2004
Accepted: 24 January 2005
Published: 28 January 2005
Proposed: Yasha Eliashberg
Seconded: Leonid Polterovich, David Gabai
Authors
Frédéric Bourgeois
Université Libre de Bruxelles
Département de Mathématiques CP 218
Boulevard du Triomphe
1050 Bruxelles
Belgium
Vincent Colin
Université de Nantes
Laboratoire de Mathématiques Jean Leray
2 rue de la Houssinière
BP 92208
44322 Nantes Cedex 3
France