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

GT home page

EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 21 Apr 2006. For the current production of this journal, please refer to