Linearly controlled asymptotic dimension of the fundamental group of a graph-manifold

Smirnov, A.

doi:10.1090/S1061-0022-2011-01142-2

Linearly controlled asymptotic dimension of the fundamental group of a graph-manifold
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by A. Smirnov
Translated by: the author

St. Petersburg Math. J. 22 (2011), 307-319

DOI: https://doi.org/10.1090/S1061-0022-2011-01142-2

Published electronically: February 8, 2011

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Abstract:

We prove the estimate $\ell \text {-}\operatorname {asdim} \pi _1(M)\leq 7$ 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.

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