Geometry & Topology

Homologie de contact des variétés toroïdales

Frederic Bourgeois and Vincent Colin

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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.

R é sum é

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.

Article information

Geom. Topol., Volume 9, Number 1 (2005), 299-313.

Received: 25 November 2004
Accepted: 24 January 2005
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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.)

Contact structures Reeb fields contact homology toroidal manifolds Weinstein conjecture


Bourgeois, Frederic; Colin, Vincent. Homologie de contact des variétés toroïdales. Geom. Topol. 9 (2005), no. 1, 299--313. doi:10.2140/gt.2005.9.299.

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