Structures de contact en dimension trois et bifurcations des feuilletages de surfaces
Structures de contact en dimension trois et bifurcations des feuilletages de surfaces
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DOI：
10.1007/s002220000082
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发表时间：
1999-08
影响因子：
3.1
通讯作者：
Emmanuel Giroux
中科院分区：
文献类型：
--
作者：
Emmanuel Giroux
本文的主要目的是对某些三维流形，即透镜空间、圆上的大多数环面丛、实心环面和加厚环面T^2 x [0，1]上的切触结构进行分类。这种分类完成了早期的工作（由Etnyre [math.DG/9812065]，Eliashberg，Kanda，Makar-Limanov和作者），并从两种技术的组合中产生：手术，产生许多接触结构，以及断层扫描，允许分析先验的接触结构并从中创建组合图像。手术方法是基于Y. Eliashberg -- revisited by R. Gompf [math.GT/9803019] --并在闭流形上产生全纯可填充的接触结构。层析成像理论，在第2部分和第3部分中开发，借鉴了作者介绍的概念，并产生了少量的可能模型，用于上面列出的每个流形上的接触结构。
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.