#### Geometry & Topology, Vol. 9 (2005)
Paper no. 37, pages 1639--1676.

## K- and L-theory of the semi-direct product of the discrete 3-dimensional Heisenberg group by Z/4

### Wolfgang Lueck

**Abstract**.
We compute the group homology, the topological K-theory of the reduced
C^*-algebra, the algebraic K-theory and the algebraic 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-->K-->G-->Q-->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.
**Keywords**.
K- and L-groups of group rings and group C^*-algebras, three-dimensional Heisenberg group.

**AMS subject classification**.
Primary: 19K99.
Secondary: 19A31, 19B28, 19D50, 19G24, 55N99.

**E-print:** `arXiv:math.KT/0412156`

**DOI:** 10.2140/gt.2005.9.1639

Submitted to GT on 8 December 2004.
Paper accepted 19 August 2005.
Paper published 28 August 2005.

Notes on file formats
Wolfgang Lueck

Fachbereich Mathematik, Universitaet Muenster

Einsteinstr. 62, 48149 Muenster, Germany

Email: lueck@math.uni-muenster.de

URL: www.math.uni-muenster.de/u/lueck/

GT home page

## Archival Version

**These pages are not updated anymore.
They reflect the state of
.
For the current production of this journal, please refer to
http://msp.warwick.ac.uk/.
**