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On constructions preserving the asymptotic topology of metric spaces
We prove that graph products constructed over infinite graphs with bounded
clique number preserve finite asymptotic dimension. We also study the extent to
which Dranishnikov's property C, and Dranishnikov and Zarichnyi's straight
finite decomposition complexity are preserved by constructions such as unions,
free products, and group extensions.Comment: 13 pages, accepted for publication in NC Journal of Mathematics and
Statistic
Asymptotic Dimension
The asymptotic dimension theory was founded by Gromov in the early 90s. In
this paper we give a survey of its recent history where we emphasize two of its
features: an analogy with the dimension theory of compact metric spaces and
applications to the theory of discrete groups.Comment: Added some remarks about coarse equivalence of finitely generated
groups
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