2004/04/27 by Arthur Bartels, Bartels, Arthur, Wolfgang Lueck +1 · 2 citations
Mathematics · #19A31 #19B28 #19DXX #46L80 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.KT #msc:19A31 #msc:19B28 #msc:19DXX #msc:46L80
paper · pdf · doi:10.48550/arxiv.math/0404486
26 pages, to appear in Forum Math
openalex publication_date 2004/04/27 · arxiv created 2005/09/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Farrell-Jones and the Baum-Connes Conjecture say that one can compute the algebraic K- and L-theory of the group ring and the topological K-theory of the reduced group C^*-algebra of a group G in terms of these functors for the virtually cyclic subgroups or the finite subgroups of G. By induction theory we want to reduce these families of subgroups to a smaller family, for instance to the family of subgroups which are either finite hyperelementary or extensions of finite hyperelementary groups with infinite cyclic kernel or to the family of finite cyclic subgroups. Roughly speaking, we extend the induction theorems of Dress for finite groups to infinite groups.