2013/01/06 by Mathias Fuchs, Fuchs, Mathias
Mathematics · #19L47 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.KT #msc:19L47
paper · pdf · doi:10.48550/arxiv.1301.1059
16 pages; this version has been submitted (up to cosmetic changes)
openalex publication_date 2013/01/06 · arxiv created 2013/05/13 · arxiv updated 2013/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We compute the equivariant K-homology of the groups PSL2 of imaginary quadratic integers with trivial and non-trivial class-group. This was done before only for cases of trivial class number. We rely on reduction theory in the form of the Γ-CW-complex defined by Flöge. We show that the difficulty arising from the non-proper action of Γ on this complex can be overcome by considering a natural short exact sequence of C^∗-algebras associated to the universal cover of the Borel-Serre compactification of the locally symmetric space associated to Γ. We use rather elementary C^∗-algebraic techniques including a slightly modified Atiyah-Hirzebruch spectral sequence as well as several 6-term sequences. This computes the K-theory of the reduced and full group C^∗-algebras of the Bianchi groups.