It was stated by M. Gromov [Gr2] that, for any hyperbolic group G, the map from bounded cohomology Hnb(G,ℝ) to Hn(G, ℝ) induced by inclusion is surjective for n ≥ 2. We introduce a homological analogue of straightening simplices, which works for any hyperbolic group. This implies that the map Hnb (G, V) → Hn(G, V) is surjective for n ≥ 2 when V is any bounded ℚG-module and when V is any finitely generated abelian group.
ASJC Scopus subject areas
- Geometry and Topology