Low degree bounded cohomology and $L^2$-invariants for negatively curved groups

Abstract

We study the subgroup structure of discrete groups that share cohomological properties which resemble non-negative curvature. Examples include all Gromov hyperbolic groups.

We provide strong restrictions on the possible s-normal subgroups of a ‘negatively curved’ group. Another result says that the image of a group, which is boundedly generated by a finite set of amenable subgroups, in a group, which admits a proper quasi-1-cocycle into the regular representation, has to be amenable. These results extend to a certain class of randomorphisms in the sense of Monod.