• DOI:10.1007/s002220000082
• Corpus ID: 119633412

Structures de contact en dimension trois et bifurcations des feuilletages de surfaces

@article{Giroux2000StructuresDC,
  title={Structures de contact en dimension trois et bifurcations des feuilletages de surfaces},
  author={Emmanuel Giroux},
  journal={Inventiones mathematicae},
  year={2000},
  volume={141},
  pages={615-689}
}

• Emmanuel Giroux
• Published 23 August 1999
• Mathematics
• Inventiones mathematicae

The main purpose of this article is to classify contact structures on some 3-manifolds, namely lens spaces, most torus bundles over a circle, the solid torus, and the thickened torus T^2 x [0,1]. This classification completes earlier work (by Etnyre [math.DG/9812065], Eliashberg, Kanda, Makar-Limanov, and the author) and results from the combination of two techniques: surgery, which produces many contact structures, and tomography, which allows one to analyse a contact structure given a priori and to create from it a combinatorial image. The surgery methods are based on a theorem of Y. Eliashberg -- revisited by R. Gompf [math.GT/9803019] -- and produces holomorphically fillable contact structures on closed manifolds. Tomography theory, developed in parts 2 and 3, draws on notions introduced by the author and yields a small number of possible models for contact structures on each of the manifolds listed above.