Alessandro Sisto

Hyperbolically embedded subgroups have been defined by
Dahmani-Guirardel-Osin and they provide a common perspective on several
classes of groups including (relatively) hyperbolic groups, mapping
class groups, many groups acting on nonpositively curved spaces, etc.
The bounded cohomology of a group is defined similarly to the usual
cohomology but considering bounded functions only, and is an invariant
related to several geometric features of a group like its actions on
negatively curved manifolds.
I will show how to use the properties of hyperbolically embedded
subgroups to get nonvanishing results for the bounded cohomology for the
aforementioned groups.
Joint with Roberto Frigerio and Maria Beatrice Pozzetti.