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.
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Acknowledgements
The authors would like to thank Hervé Oyono-Oyono for many helpful explanations.
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This work was supported by the National Natural Science Foundation of China (Nos. 11771143, 11831006, 11420101001).
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Wang, Q., Wang, Z. Persistence Approximation Property for Maximal Roe Algebras. Chin. Ann. Math. Ser. B 41, 1–26 (2020). https://doi.org/10.1007/s11401-019-0182-0
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DOI: https://doi.org/10.1007/s11401-019-0182-0
Keywords
- Quantitative K-theory
- Persistence approximation property
- Maximal coarse Baum-Connes conjecture
- Maximal Roe algebras