Abstract.
It was stated by M. Gromov [Gr2] that, for any hyperbolic group G, the map from bounded cohomology \( H^n_b(G,{\Bbb R}) \) to \( H^n(G,{\Bbb R}) \) induced by inclusion is surjective for \( n \ge 2 \). We introduce a homological analogue of straightening simplices, which works for any hyperbolic group. This implies that the map \( H^n_b(G,V) \to H^n(G,V) \) is surjective for \( n \ge 2 \) when V is any bounded \( {\Bbb Q}G \)-module and when V is any finitely generated abelian group.
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Submitted: February 2000, Revised version: February 2001.
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Mineyev, I. Straightening and bounded cohomology of hyperbolic groups . GAFA, Geom. funct. anal. 11, 807–839 (2001). https://doi.org/10.1007/PL00001686
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DOI: https://doi.org/10.1007/PL00001686