Singular Riemannian foliation

奇异黎曼叶理

• 批准号: 43659494
• 负责人: Dr. Dirk Töben
• 金额: --
• 依托单位: Department of Mathematics
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2007
• 资助国家: 德国
• 起止时间: 2006-12-31 至 2009-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/43659494?language=en
• 关键词: Singular; Riemannian; foliation

The Poincaré-Hopf Theorem states that by properly counting the singularities of a vector field, or more precisely by adding their indices, one obtains the Euler characteristic. In modern terms this is the localization of the Euler class and the indices are residual data. For a Killing field, an infinitesimal isometric motion, Bott was able to localize polynomials of top degree in the Pontryagin classes of the manifold to its singularities, A singular Riemannian foliation is the higher dimensional analogue of a Killing field. In this project we want to derive a residue formula of the above kind for singular Riemannian foliations with special attention to those that arise as leaf closures of a Riemannian foliation. As an application we want to derive topological obstructions to the existence of a Riemannian foliation on a given manifold.

庞加莱-霍普夫定理指出，通过适当地计算向量场的奇点，或者更准确地说，通过增加它们的指数，可以获得欧拉特征线。在现代术语中，这是欧拉类的局部化，指数是残差数据。对于一个Killing场，一个无穷小的等距运动，Bott能够本地化多项式的最高程度的庞特里亚金类的歧管的奇性，一个奇异的黎曼叶理是高维类似的Killing场。在这个项目中，我们要推导出一个上述类型的剩余公式奇异黎曼叶理，特别注意那些出现的叶闭包的黎曼叶理。作为一个应用，我们想得到的拓扑障碍存在的黎曼叶状在一个给定的流形。