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

Lueck, Wolfgang¹

¹ Fachbereich Mathematik, Universität Münster, Einsteinstr. 62, 48149 Münster, Germany

Geometry & topology, Tome 9 (2005) no. 3, pp. 1639-1676.

Résumé

We compute the group homology, the topological $K$–theory of the reduced $C^{\ast }$–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 $\mathbb{Z}∕4$. 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.

Détail

DOI : 10.2140/gt.2005.9.1639

Keywords: $K$– and $L$–groups of group rings and group $C^*$–algebras, three-dimensional Heisenberg group

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