### Induction Theorems and Isomorphism Conjectures for K- and L-Theory, by Arthur Bartels and Wolfgang Lueck

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.

Arthur Bartels <bartelsa@math.uni-muenster.de>

Wolfgang Lueck <lueck@math.uni-muenster.de>