Linearly controlled asymptotic dimension of the fundamental group of a graph-manifold
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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.References
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Bibliographic Information
- A. Smirnov
- Affiliation: Mathematics and Mechanics Department, St. Petersburg State University, 28 Universitetskii Prospekt, Peterhoff, St. Petersburg 198504, Russia
- ORCID: 0000-0002-6781-2105
- Email: alvismi@gmail.com
- Received by editor(s): April 23, 2009
- Published electronically: February 8, 2011
- © Copyright 2011 American Mathematical Society
- Journal: St. Petersburg Math. J. 22 (2011), 307-319
- MSC (2010): Primary 57M50, 55M10; Secondary 05C05, 20F69
- DOI: https://doi.org/10.1090/S1061-0022-2011-01142-2
- MathSciNet review: 2668128