Straightening and bounded cohomology of hyperbolic groups

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)807-839
Number of pages33
JournalGeometric and Functional Analysis
Volume11
Issue number4
DOIs
StatePublished - Jan 1 2001
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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