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

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.

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper37.abs.html

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• On the Farrell-Jones Conjecture and its applications
• On the Farrell-Jones and related Conjectures
• Equivariant $K$-homology for hyperbolic reflection groups
• Bredon Cohomology, K theory and K homology of Pullbacks of groups
• Rational equivariant K-homology of low dimensional groups
• On the K- and L-theory of hyperbolic and virtually finitely generated abelian groups
• Topological Rigidity for FJ by the Infinite Cyclic Group