Groups, Geometry, and Dynamics


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Volume 3, Issue 2, 2009, pp. 343–358
DOI: 10.4171/GGD/60

Published online: 2009-06-30

Low degree bounded cohomology and L2-invariants for negatively curved groups

Andreas Thom[1]

(1) Technische Universität Dresden, Germany

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.

Keywords: Hyperbolic group, higher rank lattice, property (T), orbit equivalence, ℓ2-invariants, bounded cohomology

Thom Andreas: Low degree bounded cohomology and L2-invariants for negatively curved groups. Groups Geom. Dyn. 3 (2009), 343-358. doi: 10.4171/GGD/60