Geometry & Topology 9 (2005) 299–313

DOI: 10.2140/gt.2005.9.299

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

Primary: 53D35

Secondary: 53C15

References

Publication

Received: 25 November 2004
Accepted: 24 January 2005
Published: 28 January 2005
Proposed: Yasha Eliashberg
Seconded: Leonid Polterovich, David Gabai

Authors