Permanence of metric sparsification property under finite decomposition complexity

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• 作者：Qin Wang (1)
  Wenjing Wang (2)
  Xianjin Wang (3)
  
• 关键词：Metric space ; Metric sparsification ; Asymptotic dimension ; Decomposition complexity ; Permanence property ; 46L89 ; 54E35 ; 20F65
• 刊名：Chinese Annals of Mathematics - Series B
• 出版年：2014
• 出版时间：September 2014
• 年：2014
• 卷：35
• 期：5
• 页码：751-760
• 全文大小：199 KB
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  7. Gromov, M., Asymptotic invariants of infinite groups, Geometric Group Theory, Vol. 2, London Math. Soc., Lecture Notes Series, Vol. 182, G. A. Niblo and M. A. Roller (eds.), Cambridge University Press, Cambridge, 1993.
  8. Guentner, E., Higson, N. and Weinberger, S., The Novikov conjecture for linear groups, / Publ. Math. Inst. Hautes Tudes Sci., 101(1), 2005, 243鈥?68. CrossRef
  9. Guentner, E., Tessera, R. and Yu, G. L., A notion of geometric complexity and its application to topological rigidity, / Invent. Math., 189(2), 2011, 1鈥?3.
  10. Guentner, E., Tessera, R. and Yu, G. L., Operator norm localization for linear groups and its applications to / K-Theory, / Adv. Math., 226(4), 2011, 3495鈥?510. CrossRef
  
• 作者单位：Qin Wang (1)
  Wenjing Wang (2)
  Xianjin Wang (3)
  
  1. Research Center for Operator Algebras, Department of Mathematics, East China Normal University, Shanghai, 200241, China
  2. Department of Applied Mathematics, Donghua University, Shanghai, 201620, China
  3. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China
  
• ISSN：1860-6261

文摘

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.