1993/01/01 by Alejandro Ádem, Alejandro Adem · 18 citations
Computer Science · Mathematics · #Cohomological dimension #Cohomology #Cohomology ring #Dimension (graph theory) #Discrete mathematics #Equivariant cohomology #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematics #Order (exchange) #Pure mathematics #Representation theory #Ring (chemistry) #Topological and Geometric Data Analysis #Type (biology) #math.AT #math.KT
paper · pdf · doi:10.1007/bf01232678
published in Inventiones mathematicae 114(1), 489-514 (Springer Science+Business Media) · 4 pages
arxiv created 1993/01/01 · openalex publication_date 1993/12/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Let Γ be a discrete group of finite virtual cohomological dimension with certain finiteness conditions of the type satisfied by arithmetic groups. We define a representation ring for Γ, determined on its elements of finite order, which is of finite type. Then we determine the contribution of this ring to the topological K-theory K^*(BΓ), obtaining an exact formula for the difference in terms of the cohomology of the centralizers of elements of finite order in Γ.