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Localization Algebras and Duality |
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| Authors: | Chen Xiaoman; Wang Qin |
| Institution: | Laboratory of Mathematics for Nonlinear Sciences and Institute of Mathematics, Fudan University Shanghai 200433, China xchen{at}fudan.edu.cn Laboratory of Mathematics for Nonlinear Sciences, Fudan University Shanghai 200433, China Department of Applied Mathematics, Dong Hua University Shanghai 200051, China qwang{at}dhu.edu.cn |
| Abstract: | The paper studies the dual algebras of localization Roe algebrasover proper metric spaces and develops a localization versionof Paschke duality for K-homology. It is shown that the localizationK-homology groups are isomorphic to Kasparov's K-homology groupsfor the Rips complex of proper metric spaces with bounded geometry.It follows that the obstruction groups to the coarse Baum–Connesconjecture can also be derived from the dual localization algebras. |
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