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arXiv · 1002.4365

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

Paul D. Mitchener
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Abstract

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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Paul D. Mitchener. 2010-12-07. The $K$-theory spectrum of the reduced group $C^\ast$-algebra is a functor. https://arxiv.org/abs/1002.4365

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