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| Permanence of Metric Sparsification Property underFinite Decomposition Complexity |
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Citation： |
Qin WANG,Wenjing WANG,Xianjin WANG.Permanence of Metric Sparsification Property underFinite Decomposition Complexity[J].Chinese Annals of Mathematics B,2014,35(5):751~760 |
| Page view： 1298
Net amount： 909 |
Authors： |
Qin WANG; Wenjing WANG; Xianjin WANG; |
Foundation： |
the National Natural Science Foundation of China (Nos. 11231002,
10971023, 10901033, 61104154), the Fundamental Research Funds for Central Universities of China
and the Shanghai Shuguang Project (No. 07SG38). |
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| Abstract： |
The notions of metric sparsification property and finite decomposition complexity
are recently introduced in metric geometry to study the coarse Novikov conjecture
and the stable Borel conjecture. In this paper, it is proved that a metric space X has finite
decomposition complexity with respect to metric sparsification property if and only if X
itself has metric sparsification property. As a consequence, the authors obtain an alternative
proof of a very recent result by Guentner, Tessera and Yu that all countable linear
groups have the metric sparsification property and hence the operator norm localization
property. |
Keywords： |
Metric space, Metric sparsification, Asymptotic dimension, Decomposition
complexity, Permanence property |
Classification： |
46L89, 54E35, 20F65 |
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