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.

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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/

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