图流形基本群的线性控制渐近维数
Linearly-controlled asymptotic dimension of the fundamental group of a graph-manifold
摘要：
证明了任意三维图流形的基本群的线性控制渐近维数不超过7。作为应用，我们得到了这样的图流形的泛覆盖是绝对Lipschitz收缩，并且它允许拟对称嵌入到8个度量树的乘积中。
英文摘要：
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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