论文标题
分层空间的H原则
h-Principle for Stratified Spaces
论文作者
论文摘要
我们将Gromov和Eliashberg-Mishachev的H原则扩展到了分层空间。这是在Gromov的捆绑理论框架和Eliashberg-Mishachev的光滑喷气机框架中完成的。概括涉及开发1）分层连续滑轮的概念，以扩展格罗莫夫的理论，2）平滑分层束的概念以扩展Eliashberg-Mishachev的理论。一个新功能是同型纤维滑轮的角色。我们特别表明，分层连续滑轮的层次柔韧性以及同型纤维束带的柔韧性提供了参数H原则。我们将Eliashberg-Mishachev载体近似定理扩展到分层空间。我们还证明了Smale-Hirsch浸入定理的分层类似物。
We extend Gromov and Eliashberg-Mishachev's h-principle on manifolds to stratified spaces. This is done in both the sheaf-theoretic framework of Gromov and the smooth jets framework of Eliashberg-Mishachev. The generalization involves developing 1) the notion of stratified continuous sheaves to extend Gromov's theory, 2) the notion of smooth stratified bundles to extend Eliashberg-Mishachev's theory. A new feature is the role played by homotopy fiber sheaves. We show, in particular, that stratumwise flexibility of stratified continuous sheaves along with flexibility of homotopy fiber sheaves furnishes the parametric h-principle. We extend the Eliashberg-Mishachev holonomic approximation theorem to stratified spaces. We also prove a stratified analog of the Smale-Hirsch immersion theorem.
