Geometry & Topology

Homologie de contact des variétés toroïdales

Frederic Bourgeois and Vincent Colin

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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.

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513799567

Digital Object Identifier
doi:10.2140/gt.2005.9.299

Mathematical Reviews number (MathSciNet)
MR2116317

Zentralblatt MATH identifier
1077.53070

Subjects
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.)

Keywords
Contact structures Reeb fields contact homology toroidal manifolds Weinstein conjecture

Citation

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. https://projecteuclid.org/euclid.gt/1513799567


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References

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