2010/02/23 by Paul D. Mitchener, Mitchener, Paul D.
Mathematics · #46L80 #46M15 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.1002.4365
openalex publication_date 2010/02/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We construct C^∗-categories that are anologues of the categories used in controlled algebraic K-theory. We then show that the reduced C^∗-algebra of a finitely presented group and an associated controlled C^∗-category have equivalent K-theory spectra, and that, at least in certain special cases, the associated C^∗-category depends functorially on the group. Thus in these cases the K-theory spectrum of the reduced group C^∗-algebra is a functor.