Permanence of Metric Sparsification Property under Finite Decomposition Complexity  

作　　者：Qin WANG Wenjing WANG Xianjin WANG 

机构地区：[1]Research Center for Operator Algebras, Department of Mathematics, East China Normal University [2]Department of Applied Mathematics, Donghua University [3]College of Mathematics and Statistics, Chongqing University

出　　处：《Chinese Annals of Mathematics,Series B》2014年第5期751-760,共10页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.11231002,10971023,10901033,61104154);the Fundamental Research Funds for Central Universities of China;the Shanghai Shuguang Project(No.07SG38)

摘　　要：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.

关 键 词：Metric space Metric sparsification Asymptotic dimension Decomposi- tion complexity Permanence property 

分 类 号：O189.11[理学—数学]