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Fiberwise KK-equivalence of continuous fields of C*-algebras

Published online by Cambridge University Press:  28 May 2008

Marius Dadarlat
Marius Dadarlat
Affiliation:
Department of Mathematics, Purdue University, West Lafayette IN 47907, U.S.A., mdd@math.purdue.edu.
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Abstract

Let A and B be separable nuclear continuous C(X)-algebras over a finite dimensional compact metrizable space X. It is shown that an element σ of the parametrized Kasparov group KKX(A,B) is invertible if and only all its fiberwise components σx ∈ KK(A(x),B(x)) are invertible. This criterion does not extend to infinite dimensional spaces since there exist nontrivial unital separable continuous fields over the Hilbert cube with all fibers isomorphic to the Cuntz algebra . Several applications to continuous fields of Kirchberg algebras are given. It is also shown that if each fiber of a separable nuclear continuous C(X)-algebra A over a finite dimensional locally compact space X satisfies the UCT, then A satisfies the UCT.

Keywords

Continuous fieldsK-theoryCuntz algebrasKirchberg algebras
Type
Research Article
Information
Journal of K-Theory , Volume 3 , Issue 2 , April 2009 , pp. 205 - 219
Copyright
Copyright © ISOPP 2009

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