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Chinese Annals of Mathematics, Series B

, Volume 41, Issue 1, pp 1–26 | Cite as

Persistence Approximation Property for Maximal Roe Algebras

  • Qin Wang
  • Zhen WangEmail author
Article
  • 7 Downloads

Abstract

Persistence approximation property was introduced by Hervé Oyono-Oyono and Guoliang Yu. This property provides a geometric obstruction to Baum-Connes conjecture. In this paper, the authors mainly discuss the persistence approximation property for maximal Roe algebras. They show that persistence approximation property of maximal Roe algebras follows from maximal coarse Baum-Connes conjecture. In particular, let X be a discrete metric space with bounded geometry, assume that X admits a fibred coarse embedding into Hilbert space and X is coarsely uniformly contractible, then C*max(X) has persistence approximation property. The authors also give an application of the quantitative K-theory to the maximal coarse Baum-Connes conjecture.

Keywords

Quantitative K-theory Persistence approximation property Maximal coarse Baum-Connes conjecture Maximal Roe algebras 

2000 MR Subject Classification

46L80 46L89 51F99 

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Notes

Acknowledgements

The authors would like to thank Hervé Oyono-Oyono for many helpful explanations.

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Copyright information

© The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2020

Authors and Affiliations

  1. 1.Research Center for Operator Algebras, School of Mathematical Sciences, Shanghai Key Laboratory of Pure Mathematics and Mathematical PracticeEast China Normal UniversityShanghaiChina
  2. 2.Research Center for Operator Algebras, School of Mathematical SciencesEast China Normal UniversityShanghaiChina

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