Bldg. 20.30, SR 2.058

24.07.2025

Caterina Campagnolo

15:45 Uhr

Bounded cohomology is an invariant of groups and spaces first introduced by Johnson in the 70s in the context of Banach algebras and then mightily developed by Gromov in the 80s. Since then it has been widely studied and proved useful in several areas, from geometry and topology to group theory. Its vanishing and non-vanishing depending on the family of coefficients under consideration allows one to characterize for instance finite, amenable, and Gromov hyperbolic groups.

We will present a result obtained jointly with F. Fournier-Facio, Y. Lodha and M. Moraschini on the vanishing of the bounded cohomology of the "generic enumerated group": in a natural model for countable groups, the vanishing of the bounded cohomology with a large family of coefficients is a generic property. This is in contrast to other models such as the few-relator model, that typically produce Gromov hyperbolic groups and hence with non-vanishing bounded cohomology.