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This article is cited in 3 scientific papers (total in 3 papers)
Research Papers
Linearly controlled asymptotic dimension of the fundamental group of a graph-manifold
A. Smirnov St. Petersburg State University, Department of Mathematics and Mechanics, St. Petersburg, Russia
Abstract:
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.
Received: 20.05.2009
Citation:
A. Smirnov, “Linearly controlled asymptotic dimension of the fundamental group of a graph-manifold”, Algebra i Analiz, 22:2 (2010), 185–203; St. Petersburg Math. J., 22:2 (2011), 307–319
Linking options:
https://www.mathnet.ru/eng/aa1181 https://www.mathnet.ru/eng/aa/v22/i2/p185
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Abstract page: | 350 | Full-text PDF : | 87 | References: | 50 | First page: | 6 |
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