Bounded cohomology is a metrically enriched variant of singular cohomology, constructed by replacing ordinary cochains by bounded ones. This leads to an invariant behaving very differently from singular cohomology, which is interesting both for studying topological spaces and groups.
In this talk we will at first present en detail several descriptions of bounded cohomology and derive a number of elementary properties. In the second part, we give an overview of some of the most interesting results in the subject and a few of its applications.
Matthias Blank, Universität Regensburg