Geometry & Topology 9 (2005) 1639–1676

DOI: 10.2140/gt.2005.9.1639

arXiv: math.KT/0412156

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

Mathematical Subject Classification

Primary: 19K99

Secondary: 19A31, 19B28, 19D50, 19G24, 55N99

References

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Publication

Received: 8 December 2004
Accepted: 19 August 2005
Published: 28 August 2005
Proposed: Gunnar Carlsson
Seconded: Ralph Cohen, Bill Dwyer

Authors