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arXiv · 1709.01119

Decomposition theorems for asymptotic property C and property A

G. Bell·D. Głodkowski·A. Nagórko
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Abstract

We combine aspects of the notions of finite decomposition complexity and asymptotic property C into a notion that we call finite APC-decomposition complexity. Any space with finite decomposition complexity has finite APC-decomposition complexity and any space with asymptotic property C has finite APC-decomposition complexity. Moreover, finite APC-decomposition complexity implies property A for metric spaces. We also show that finite APC-decomposition complexity is preserved by direct products of groups and spaces, amalgamated products of groups, and group extensions, among other constructions.

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G. Bell, D. Głodkowski, A. Nagórko. 2017-09-04. Decomposition theorems for asymptotic property C and property A. https://arxiv.org/abs/1709.01119

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