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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

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


Author: A. Smirnov
Translated by: the author
Original publication: Algebra i Analiz, tom 22 (2010), nomer 2.
Journal: St. Petersburg Math. J. 22 (2011), 307-319
MSC (2010): Primary 57M50, 55M10; Secondary 05C05, 20F69
Published electronically: February 8, 2011
MathSciNet review: 2668128
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove the estimate $ \ell$-$ \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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Additional Information

A. Smirnov
Affiliation: Mathematics and Mechanics Department, St. Petersburg State University, 28 Universitetskii Prospekt, Peterhoff, St. Petersburg 198504, Russia
Email: alvismi@gmail.com

DOI: http://dx.doi.org/10.1090/S1061-0022-2011-01142-2
PII: S 1061-0022(2011)01142-2
Keywords: Graph-manifold, asymptotic dimension
Received by editor(s): April 23, 2009
Published electronically: February 8, 2011
Article copyright: © Copyright 2011 American Mathematical Society