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

Alexander Smirnov

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arXiv · 0909.1098

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

Alexander Smirnov

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Abstract

We prove that the linearly controlled asymptotic dimension of the fundamental group of any 3-dimensional graph-manifold does not exceed 7. As applications we obtain that the universal cover of such a graph-manifold is an absolute Lipschitz retract and it admits a quasisymmetric embedding into the product of 8 metric trees.

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Alexander Smirnov. 2009-09-06. Linearly-controlled asymptotic dimension of the fundamental group of a graph-manifold. https://arxiv.org/abs/0909.1098

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