Bounded cohomology can be constructed similarly to singular cohomology by considering bounded cochains instead of ordinary ones. A relative version can then be derived from bounded cohomology in the same fashion as relative cohomology is derived from singular cohomology. Originally introduced by Misha Gromov, this approach leads to vector spaces carrying interesting information in the form of a semi-norm.

There have been several more recent efforts to describe relative bounded cohomology in an algebraically more accessible setting, but constructing the correct semi-norm turns out to be a non-trivial problem in general.

In this talk, we will discuss several of these approaches and present some related results and applications.

*Matthias Blank, Universität Regensburg *