Stability in bounded cohomology for classical groups

Homological stability is a phenomenon that has been studied and established in the context of ordinary group homology for several infinite ascending series of groups. So far the only existing stability result known for bounded cohomology, by Monod, concerned the families of the general and special linear groups over any local field. In this talk we present an argument that proves stability for the symplectic families over the fields of real and of complex numbers. We first describe a general method that guarantees bounded-cohomological stability along a series of locally compact second-countable groups, provided that there exists a family of highly connected complexes on which the groups have a highly transitive action. Then, we introduce a new family of complexes associated to the symplectic groups, which we call symplectic Stiefel complexes. Similar kinds of objects can be defined for other families of classical groups.
This is joint work with Tobias Hartnick.