Volume 9, issue 3 (2005)

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$K$– and $L$–theory of the semi-direct product of the discrete 3–dimensional Heisenberg group by $\mathbb{Z}/4$

Wolfgang Lueck

Geometry & Topology 9 (2005) 1639–1676

arXiv: math.KT/0412156


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 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.

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$K$– and $L$–groups of group rings and group $C^*$–algebras, three-dimensional Heisenberg group
Mathematical Subject Classification 2000
Primary: 19K99
Secondary: 19A31, 19B28, 19D50, 19G24, 55N99
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Received: 8 December 2004
Accepted: 19 August 2005
Published: 28 August 2005
Proposed: Gunnar Carlsson
Seconded: Ralph Cohen, Bill Dwyer
Wolfgang Lueck
Fachbereich Mathematik
Universität Münster
Einsteinstr. 62
48149 Münster