Geometry & Topology

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

Wolfgang Lueck

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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 4. These computations will follow from the more general treatment of a certain class of groups G which occur as extensions 1KGQ1 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.

Article information

Source
Geom. Topol., Volume 9, Number 3 (2005), 1639-1676.

Dates
Received: 8 December 2004
Accepted: 19 August 2005
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513799645

Digital Object Identifier
doi:10.2140/gt.2005.9.1639

Mathematical Reviews number (MathSciNet)
MR2175154

Subjects
Primary: 19K99: None of the above, but in this section
Secondary: 19A31: $K_0$ of group rings and orders 19B28: $K_1$of group rings and orders [See also 57Q10] 19D50: Computations of higher $K$-theory of rings [See also 13D15, 16E20] 19G24: $L$-theory of group rings [See also 11E81] 55N99: None of the above, but in this section

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

Citation

Lueck, Wolfgang. $K$– and $L$–theory of the semi-direct product of the discrete 3–dimensional Heisenberg group by $\mathbb{Z}/4$. Geom. Topol. 9 (2005), no. 3, 1639--1676. doi:10.2140/gt.2005.9.1639. https://projecteuclid.org/euclid.gt/1513799645


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