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Published: 
October 13, 2000

Keywords: 
C*algebras, KKtheory, continuous fields

Subject: 
19K35, 46L35

Abstract:

A structural description is given of the separable
$C^*$algebras that are contractible in KKtheory or Etheory.
Subsequently it is shown that two separable $C^*$algebras, $A$ and $B$,
are KKequivalent if and only if there is a bundle of separable
$C^*$algebras over $[0,1]$ which is piecewise trivial with no more than
six points of nontriviality such that the kernel of each fiber map is
KKcontractible, all fiber maps are semisplit and such that the fibers
at the endpoints of the interval are $A$ and $B$.

Author information:
Institut for Matematiske Fag, Ny Munkegade, 8000 Aarhus C, Denmark
matkt@imf.au.dk
 