Vortrag von Natalie Peternell (Freiburg)

In my talk I will start with an introduction to smooth Deligne cohomology and then present the main results of my diploma thesis.
Let G be a compact connected Lie group with classifying space BG and let a be an integer cohomology class of even degree p on BG. Let F be a compact connected differentiable manifold with G-action satisfying further topological conditions, e.g. F is a Stiefel manifold. Suppose that a is the image under transgression in the universal G-principal bundle of a certain cohomology class on F. Given any G-principal bundle E on a compact manifold M, I will explain some of the main steps how to construct explicitly a natural class in Deligne cohomology which represents the a-characteristic class of the bundle E.
At the end I will dicuss some examples of characteristic classes which satisfy the assumptions made in the main theorem of my diploma thesis.