Georg Frenck, Karlsruhe Institute of Technology

Title: Characteristic classes of manifold-bundles over spheres

Abstract: Manifold bundles with fiber M are classified by the classifying space of it diffeomorphism group Diff(M). Hence, the cohomology of this classifying space is the ring of characteristic classes for manifold bundles. In this talk I will describe which rational characteristic classes are attained by manifold bundles over spheres. As an application, one can deduce the existence of many fiber bundles where base and fiber both admit positive scalar, Ricci and even sectional curvature, whereas the total space does not.