Asymptotic dimension of relatively hyperbolic groups

2004/11/25 by Denis Osin, D. V. Osin, Osin, D. V. · 3 citations
Mathematics · #Advanced Operator Algebra Research #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.GR #msc:20F67 #msc:20F69

paper · pdf · doi:10.48550/arxiv.math/0411585

The proof of the main result is simplified, some misprints are corrected

arxiv created 2005/05/04 · arxiv updated 2009/12/01

Abstract

Suppose that a finitely generated group G is hyperbolic relative to a collection of subgroups \H₁, ..., H_m\ . We prove that if each of the subgroups H₁, ..., H_m has finite asymptotic dimension, then asymptotic dimension of G is also finite.

Cited by

• Uniform embeddability of relatively hyperbolic groups
• The twisted coarse Baum--Connes conjecture and relative hyperbolic groups
• A simple criterion for non-relative hyperbolicity and one-endedness of groups

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