Cristina Pagliantini: Relative (continuous) bounded cohomology

The understanding of bounded cohomology of a space is mostly based on the relationship between bounded cohomology of spaces and of groups established by Gromov, Ivanov (and by Monod in the case of continuous cohomology). In the relative context, starting from a definition of bounded cohomology of pairs of groups due to Gromov, we provide an extension of Gromov's, Ivanov's and Monod's results for pairs of topological spaces. As an application we sketch a proof of the fact that measure homology coincides with singular homology for a wide class of topological pairs (in the absolute case this is a result by Löh). This is joint work with Roberto Frigerio.