Straightening and bounded cohomology of hyperbolic groups

Igor Mineyev

doi:10.1007/PL00001686

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 Hⁿ_b(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 Hⁿ_b (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 language	English (US)
Pages (from-to)	807-839
Number of pages	33
Journal	Geometric and Functional Analysis
Volume	11
Issue number	4
DOIs	https://doi.org/10.1007/PL00001686
State	Published - 2001
Externally published	Yes

ASJC Scopus subject areas

Analysis
Geometry and Topology

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10.1007/PL00001686

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Straightening and bounded cohomology of hyperbolic groups

Abstract

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