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On the quasidiagonality of roe algebras

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Science China Mathematics 2011年第5期54卷 1011-1018页

作者： WEI ShuYun Department of Mathematics Soochow University Suzhou 215006 China

Let X be a noncompact discrete metric space with bounded geometry. Associated with X are two C*-algebras, the so-called uniform roe algebra B*(X) and coarse roe algebra C*(X), which arose from the index theory on noncompact complete Riemannian manifolds. In this paper, we describe the quasidiagonality of B*(X) and C*(X) in terms of coarse geometric invariants. Some necessary and suficient conditions are given, which involve the Fredholm index and coarse connectedness of metric spaces.

关键词： roe algebra quasidiagonality coarse geometry

Relative equivariant coarse index and relative L^(2)-index

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Science China Mathematics 2023年第7期66卷 1449-1472页

作者： Xiaoman Chen Yanlin Liu Dapeng Zhou School of Mathematical Sciences Fudan UniversityShanghai 200433China School of Statistics and Information Shanghai University of International Business and EconomicsShanghai 201620China Research Center for Operator algebras East China Normal UniversityShanghai 200062China

In this paper,we define a relative equivariant coarse index for proper actions and a relative L^(2)-*** derive a relative equivariant coarse index theorem connecting the relative equivariant coarse index with the localized equivariant coarse ***,we present a calculation formula on the relative L^(2)-index and provide a relative L^(2)-index *** work is an expansion of the relative index theory which reflects the difference between two manifolds.

关键词： relative equivariant coarse index relative L^(2)-index regular cover roe algebra

Remarks on the Operator Norm Localization Property

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Chinese Annals of Mathematics,Series B 2011年第4期32卷 593-604页

作者： Xianjin WANG Department of Applied Mathematics Donghua University Shanghai 201620 China.

The author studies the metric spaces with operator norm localization property. It is proved that the operator norm localization property is coarsely invariant and is preserved under certain infinite union. In the case... 详细信息

关键词： Metric space Asymptotic dimension Operator norm localization Coarse invariance roe algebra

Geometric Property(T)

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Chinese Annals of Mathematics,Series B 2014年第5期35卷 761-800页

作者： Rufus WILLETT Guoliang YU Department of Mathematics University of Hawai’i at Mānoa Department of Mathematics Texas A&M University Shanghai Center for Mathematical Sciences

This paper discusses "geometric property(T)". This is a property of metric spaces introduced in earlier works of the authors for its applications to K-theory. Geometric property(T) is a strong form of "expansion property", in particular, for a sequence(Xn)of bounded degree finite graphs, it is strictly stronger than(Xn) being an expander in the sense that the Cheeger constants h(Xn) are bounded *** this paper, the authors show that geometric property(T) is a coarse invariant,i.e., it depends only on the large-scale geometry of a metric space X. The authors also discuss how geometric property(T) interacts with amenability, property(T) for groups,and coarse geometric notions of a-T-menability. In particular, it is shown that property(T) for a residually finite group is characterised by geometric property(T) for its finite quotients.

关键词： Coarse geometry Expander roe algebra Property (T)