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 pers...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 Cmax*(X) has persistence approximation property. The authors also give an application of the quantitative K-theory to the maximal coarse Baum-Connes conjecture.展开更多
In this paper,the authors study the persistence approximation property for quantitative K-theory of filtered L^(p)operator algebras.Moreover,they define quantitative assembly maps for L^(p)operator algebras when p∈[1...In this paper,the authors study the persistence approximation property for quantitative K-theory of filtered L^(p)operator algebras.Moreover,they define quantitative assembly maps for L^(p)operator algebras when p∈[1,∞).Finally,in the case of L^(p)crossed products and L^(p)Roe algebras,sufficient conditions for the persistence approximation property are found.This allows to give some applications involving the L^(p)(coarse)Baum-Connes conjecture.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11771143,11831006,11420101001).
文摘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 Cmax*(X) has persistence approximation property. The authors also give an application of the quantitative K-theory to the maximal coarse Baum-Connes conjecture.
基金supported by the National Natural Science Foundation of China(Nos.12271165,12171156,12301154)the Science and Technology Commission of Shanghai Municipality(No.22DZ2229014).
文摘In this paper,the authors study the persistence approximation property for quantitative K-theory of filtered L^(p)operator algebras.Moreover,they define quantitative assembly maps for L^(p)operator algebras when p∈[1,∞).Finally,in the case of L^(p)crossed products and L^(p)Roe algebras,sufficient conditions for the persistence approximation property are found.This allows to give some applications involving the L^(p)(coarse)Baum-Connes conjecture.
