On constructions preserving the asymptotic topology of metric spaces

Abstract

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.

13 pages, accepted for publication in NC Journal of Mathematics and Statistics

References in corpus (3)

• The Haagerup property is stable under graph products
• Weak coherence of groups and finite decomposition complexity
• Groups Acting on Metric Spaces with Asymptotic Property C

Cited by in corpus (1)

• Decomposition theorems for asymptotic property C and property A