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LOCALIZATION ALGEBRAS AND DUALITY

Published online by Cambridge University Press:  24 March 2003

XIAOMAN CHEN  and
QIN WANG
XIAOMAN CHEN
Affiliation:
Laboratory of Mathematics for Nonlinear Sciences and Institute of Mathematics, Fudan University, Shanghai 200433, [email protected]
QIN WANG
Affiliation:
Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai 200433, China Department of Applied Mathematics, Dong Hua University, Shanghai 200051, [email protected]
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Abstract

The paper studies the dual algebras of localization Roe algebras over proper metric spaces and develops a localization version of Paschke duality for $K$ -homology. It is shown that the localization $K$ -homology groups are isomorphic to Kasparov's $K$ -homology groups for the Rips complex of proper metric spaces with bounded geometry. It follows that the obstruction groups to the coarse Baum–Connes conjecture can also be derived from the dual localization algebras.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 66 , Issue 1 , August 2002 , pp. 227 - 239
Copyright
The London Mathematical Society, 2002

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Footnotes

This research is supported in part by the National Basic Research Project (973), NSF and the Educational Ministry of China.