The $K$-theory spectrum of the reduced group $C^\ast$-algebra is a functor

Details The $K$-theory spectrum of the reduced group $C^\ast$-algebra is a functor The $K$-theory spectrum of the reduced group $C^\ast$-algebra is a functor

2010-02-23

arxiv.org/abs/1002.4365v3

Mathematics

K-Theory and Homology

The paper has been withdrawn due to a crucial error

Scientific paper

We construct $C^\ast$-categories that are anologues of the categories used in controlled algebraic $K$-theory. We then show that the reduced $C^\ast$-algebra of a finitely presented group and an associated controlled $C^\ast$-category have equivalent $K$-theory spectra, and that, at least in certain special cases, the associated $C^\ast$-category depends functorially on the group. Thus in these cases the $K$-theory spectrum of the reduced group $C^\ast$-algebra is a functor.

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