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Algebra i Analiz, 2010, Volume 22, Issue 2, Pages 185–203 (Mi aa1181)  

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
Full-text PDF (674 kB) Citations (3)
References:
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
English version:
St. Petersburg Mathematical Journal, 2011, Volume 22, Issue 2, Pages 307–319
DOI: https://doi.org/10.1090/S1061-0022-2011-01142-2
Bibliographic databases:
Document Type: Article
Language: Russian
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
Citation in format AMSBIB
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\by A.~Smirnov
\paper Linearly controlled asymptotic dimension of the fundamental group of a~graph-manifold
\jour Algebra i Analiz
\yr 2010
\vol 22
\issue 2
\pages 185--203
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\transl
\jour St. Petersburg Math. J.
\yr 2011
\vol 22
\issue 2
\pages 307--319
\crossref{https://doi.org/10.1090/S1061-0022-2011-01142-2}
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  • https://www.mathnet.ru/eng/aa1181
  • https://www.mathnet.ru/eng/aa/v22/i2/p185
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и анализ St. Petersburg Mathematical Journal
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    Abstract page:350
    Full-text PDF :87
    References:50
    First page:6
     
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