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Asymptotic Dimension

open access: yes, 2017
This chapter considers the notion of asymptotic dimension. It first provides an overview of asymptotic dimension before explaining the asymptotic dimensions of free abelian and nonabelian groups, free groups, groups, integers, metric spaces, and products.
Greg Bell
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On the asymptotic extension dimension

2020
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Repovs, D., Zarichnyi, ??.
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Dimension and Fundamental Groups of Asymptotic Cones

Journal of the London Mathematical Society, 1999
The goal of this paper is to study the asymptotic cones of some groups which have an exponential Dehn function, in particular, the asymptotic cone of the Baumslag-Solitar groups. Due to a result by Gromov and Drutu, groups with a simple connected asymptotic cone have a polynomial Dehn function, hence the asymptotic cones studied will have a nontrivial ...
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On the Asymptotic Homological Dimension of Hyperbolic Groups

Bulletin of the London Mathematical Society, 1995
An interesting subject, which has been recently intensively studied and publicized by \textit{M. Gromov} [in his paper ``Asymptotic invariants of infinite groups'' (Lond. Math. Soc. Lect. Note Ser. 182, 1993)] is to find quasi-isometric (or ``asymptotic'') invariants of metric spaces.
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