| Asymptotic Excisions of Metric Spaces and Ideals of Asymptotic Coarse Roe Algebras |
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| 作者姓名： | 李晋秀 王勤 |
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| 作者单位： | Department of Applied Mathematics, Donghua University, Shanghai 200051 |
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| 基金项目： | 国家自然科学基金;东华大学校科研和教改项目 |
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| 摘 要： | IntroductionTheC*-algebras associated with coarse geometry ofproper metric spacesXhave beenstudiedin recent years inthe area of index theory , see 1 , 2 , 4 , 5] . The mosti mportant one , called the Roe algebra4],is generated bylocally compact , finite propagation operators on anX-module . In view of noncommutative topology , the Roealgebra can be considered as the noncommutative quotientof coarsening a metric space by identifying all pairs ofpoints that are finite distance apart . Anothe…
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| 关 键 词： | 度量空间 接近切除 Roe算法 K理论 |
| 收稿时间： | 2005-04-21 |
Asymptotic Excisions of Metric Spaces and Ideals of Asymptotic Coarse Roe Algebras |
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| LI Jin-xiu,WANG Qin.Asymptotic Excisions of Metric Spaces and Ideals of Asymptotic Coarse Roe Algebras[J].Journal of Donghua University,2006,23(2):115-118. |
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| Authors: | LI Jin-xiu WANG Qin |
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| Abstract: | We introduce in this note the notions of asymptotic excision of proper metric spaces and asymptotic equivalence relation for subspaces of metric spaces, which are relevant in characterizing spatial ideals of the asymptotic coarse Roe algebras. We show that the lattice of the asymptotic equivalence classes of the subspaces of a proper metric space is isomorphic to the lattice of the spatial ideals of the asymptotic Roe algebra. For asymptotic excisions of the metric space, we also establish a MayeroVietoris sequence in K-theory of the asymptotic coarse Roe algebras. |
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| Keywords: | Metric spaces asymptotic excision the Roe algebra ideal K-theory |
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