Decomposition theorems for asymptotic property C and property A
Metric Geometry
2019-02-19 v3 Functional Analysis
General Topology
Group Theory
Geometric Topology
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.
Keywords
Cite
@article{arxiv.1709.01119,
title = {Decomposition theorems for asymptotic property C and property A},
author = {G. Bell and D. Głodkowski and A. Nagórko},
journal= {arXiv preprint arXiv:1709.01119},
year = {2019}
}