Wrinkling of smooth mappings III. Foliations of codimension greater than one
Wrinkling of smooth mappings III. Foliations of codimension greater than one
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平滑映射的起皱 III．
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
N. Mishachev
中科院分区：
文献类型：
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作者：
Y. Eliashberg;N. Mishachev
这是我们的皱纹传奇中的第三篇论文(见[EM1]，[EM2])。第一篇论文[EM1]专门论述了该方法的基础。第二篇论文[EM2]和本篇论文都致力于研究起皱工艺的应用。在文献[EM2]中，我们证明了关于具有中等奇异性的函数的一个推广的伊古萨定理。本文主要研究褶皱方法在面理理论中的应用。这篇论文的结果基本上与我们的论文[ME]重叠，这篇论文写于20年前，当时瑟斯顿在闭流形上发现了余维大于1的叶的h-原理(见[Th1])。文[ME]包含了来自[Th1]的瑟斯顿定理的另一种证明，并且基于在[E2]中发展的奇点外科技术。本文给出的证明是基于褶皱方法的。虽然本质上类似于我们在[ME]中的证明，但在我们看来，当前的证明更透明，更容易理解。除了瑟斯顿定理，我们在这里证明了[ME]中与叶系族有关的结果的一个推广版本。
This is the third paper in our Wrinkling saga (see [EM1], [EM2]). The first paper [EM1] was devoted to the foundations of the method. The second paper [EM2], as well as the current one are devoted to the applications of the wrinkling process. In [EM2] we proved, among other results, a generalized Igusa’s theorem about functions with moderate singularities. The current paper is devoted to applications of the wrinkling method in the foliation theory. The results of this paper essentially overlap with our paper [ME], which was written twenty years ago, soon after Thurston’s remarkable discovery (see [Th1]) of an h-principle for foliations of codimension greater than one on closed manifolds. The paper [ME] contained an alternative proof of Thurston’s theorem from [Th1], and was based on the technique of surgery of singularities which was developed in [E2]. The proof presented in this paper is based on the wrinkling method. Although essentially similar to our proof in [ME], the current proof is, in our opinion, more transparent and easier to understand. Besides Thurston’s theorem we prove here a generalized version of our results from [ME] related to families of foliations.