Geodesic
Linearly controlled asymptotic dimension of the fundamental group of a~graph-manifold
Algebra i analiz, Tome 22 (2010) no. 2, pp. 185-203.

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We prove the estimate $\ell\text{-asdim}\,\pi_1(M)\leq7$ for the linearly controlled asymptotic dimension of the fundamental group of any 3-dimensional graph-manifold $M$. As applications, we show that the universal cover $\widetilde M$ of $M$ is an absolute Lipschitz retract and admits a quasisymmetric embedding into the product of 8 metric trees.
Keywords: graph-manifold, asymptotic dimension. 
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A. Smirnov. Linearly controlled asymptotic dimension of the fundamental group of a~graph-manifold. Algebra i analiz, Tome 22 (2010) no. 2, pp. 185-203. http://geodesic.mathdoc.fr/item/AA_2010_22_2_a5/

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