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| Persistence Approximation Property for Maximal Roe Algebras |
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Citation： |
Qin WANG,Zhen WANG.Persistence Approximation Property for Maximal Roe Algebras[J].Chinese Annals of Mathematics B,2020,41(1):1~26 |
| Page view： 1223
Net amount： 1427 |
Authors： |
Qin WANG; Zhen WANG |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11771143, 11831006, 11420101001). |
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| Abstract： |
Persistence approximation property was introduced by Herv\'e
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
$C^{*}_{\rm max}(X)$ 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, Maximalcoarse Baum-Connes conjecture, Maximal Roe algebras |
Classification： |
46L80, 46L89, 51F99 |
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