Structures de contact en dimension trois et bifurcations des feuilletages de surfacesReport as inadecuate



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


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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.



Author: Emmanuel Giroux

Source: https://archive.org/







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