Singular Riemannian foliation

点击翻译按钮获取中文摘要

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.