Asymptotic coarsening of proper metric spaces and index problems

Xiaoman Chen; Qin Wang

doi:10.1007/s00229-002-0344-2

Asymptotic coarsening of proper metric spaces and index problems

Xiaoman Chen^*
, Qin Wang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We introduce an asymptotic coarse structure on proper metric spaces and study the associated C*-algebras and assembly maps. We establish an asymptotic Lipschitz homotopy invariance theorem for the K-theory of these C*-algebras and the K-homology of the metric space, and show that the assembly map is an isomorphism over an asymptotically scaleable space.

Original language	English
Pages (from-to)	475-486
Number of pages	12
Journal	Manuscripta Mathematica
Volume	110
Issue number	4
DOIs	https://doi.org/10.1007/s00229-002-0344-2
State	Published - Apr 2003
Externally published	Yes

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abstract = "We introduce an asymptotic coarse structure on proper metric spaces and study the associated C*-algebras and assembly maps. We establish an asymptotic Lipschitz homotopy invariance theorem for the K-theory of these C*-algebras and the K-homology of the metric space, and show that the assembly map is an isomorphism over an asymptotically scaleable space.",

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AB - We introduce an asymptotic coarse structure on proper metric spaces and study the associated C*-algebras and assembly maps. We establish an asymptotic Lipschitz homotopy invariance theorem for the K-theory of these C*-algebras and the K-homology of the metric space, and show that the assembly map is an isomorphism over an asymptotically scaleable space.

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Asymptotic coarsening of proper metric spaces and index problems

Abstract

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