Geometry & Topology, Vol. 9 (2005) Paper no. 9, pages 299--313.

Homologie de contact des varietes toroidales

Frederic Bourgeois and Vincent Colin

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.

Resume. On montre que l'homologie de contact distingue une infinite de structures de contact tendues sur toute variete toroidale irreductible et orientable de dimension trois. En consequence des calculs d'homologie de contact, sur une tres large classe de varietes toroidales, tous les exemples de structures de contact universellement tendues de torsion non nulle connus verifient la conjecture de Weinstein.

Keywords. Contact structures, Reeb fields, contact homology, toroidal manifolds, Weinstein conjecture

AMS subject classification. Primary: 53D35. Secondary: 53C15.

DOI: 10.2140/gt.2005.9.299

E-print: arXiv:math.GT/0411577

Submitted to GT on 25 November 2004. Paper accepted 24 January 2005. Paper published 28 January 2005.

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Frederic Bourgeois, Vincent Colin

Universite Libre de Bruxelles, Departement de Mathematiques CP 218
Boulevard du Triomphe, 1050 Bruxelles, Belgium
and
Universite de Nantes, Laboratoire de Mathematiques Jean Leray
2 rue de la Houssiniere, BP 92208, 44322 Nantes Cedex 3, France

Email: fbourgeo@ulb.ac.be, Vincent.Colin@math.univ-nantes.fr

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