A characterization of relatively hyperbolic groups via bounded\n cohomology

2015/05/17 by Federico Franceschini, Franceschini, Federico
Mathematics · #Algebraic Geometry and Number Theory #Bounded function #Characterization (materials science) #Cohomology #Combinatorics #Discrete mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Physics #Pure mathematics #Surjective function #math.GR #math.GT

paper · pdf · doi:10.48550/arxiv.1505.04465

39 pp

openalex publication_date 2015/05/17 · arxiv created 2016/11/07 · arxiv updated 2016/11/08 · openalex created_date 2022/10/03 · openalex updated_date 2026/08/05

Abstract

It was proved by Mineyev and Yaman that, if (\Γ, \Γ') is a\nrelatively hyperbolic pair, the comparison map H_b^k(
Gamma,
Gamma'; V)
to\nH^k(
Gamma,
Gamma'; V) is surjective for every k \≥ 2, and any bounded\n\Γ--module V. By exploiting results of Groves and Manning, we give\nanother proof of this result. Moreover, we prove the opposite implication under\nweaker hypotheses than the ones required by Mineyev and Yaman.\n

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