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.