Asymptotic dimension of relatively hyperbolic groups

Abstract

Suppose that a finitely generated group $G$ is hyperbolic relative to a collection of subgroups $\{H_1,...,H_m\}$. We prove that if each of the subgroups $H_1,...,H_m$ has finite asymptotic dimension, then asymptotic dimension of $G$ is also finite.

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

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• Relative property A and relative amenability for countable groups