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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00009389
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Submitted on : Sunday, October 2, 2005 - 6:31:20 PM
Last modification on : Wednesday, December 9, 2020 - 7:36:02 PM

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Emmanuel Giroux. Structures de contact en dimension trois et bifurcations des feuilletages de surfaces. 1999. ⟨hal-00009389⟩

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