Induction Theorems and Isomorphism Conjectures for K- and L-Theory

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 Z as kernel or to the family of finite cyclic subgroups. Roughly speaking, we extend the induction theorems of Dress for finite groups to infinite groups. Key words: K- and L-groups of group rings and group C ∗-algebras, induction theorems.