Computations of K- and L-Theory of Cocompact Planar Groups

The verification of the isomorphism conjectures of Baum and Connes and Farrell and Jones for certain classes of groups is used to compute the algebraic K- and L-theory and the topological K-theory of cocompact planar groups (=cocompact N.E.C-groups) and of groups G appearing in an extension where is a finite group and the conjugation -action on ⁿ is free outside . These computations apply, for instance, to two-dimensional crystallographic groups and cocompact Fuchsian groups.