K-and L-theory of the semi-direct product of the discrete Heisenberg group by Z/4, by Wolfgang Lueck

We compute the group homology, the topological K-theory of the reduced C^*-algebra and the algebraic $- and L-theory of the group ring of the semi-direct product of the three-dimensional discrete Heisenberg group by Z/4. These computations will follow from the more general treatment of a certain class of groups G which occur as extensions 1 to K to G to Q to 1 of a torsionfree group K by a group Q which satisfies certain assumptions. The key ingredients are the Baum-Connes and Farrell-Jones Conjectures and methods from equivariant algebraic topology.

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