Singular Riemannian foliation

• Applicant: Dr. Dirk Töben
• Subject Area: Mathematics
• Term: from 2007 to 2010
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 43659494

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.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1154: Global Differential Geometry
• International Connection: USA
• Participating Person: Professor Dr. Steven Hurder