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Journal of Topology Advance Access published online on October 28, 2007
Journal of Topology, doi:10.1112/jtopol/jtm008
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© 2007 London Mathematical Society

On the Farrell–Jones Conjecture and its applications

Arthur Bartels and Wolfgang Lück

Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr 62, D-48149 Münster, Germany bartelsa{at}math.uni-muenster.de, lueck{at}math.uni-muenster.de

Holger Reich

Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, Universitätsstr 1, D-40225 Düsseldorf, Germany holger.reich{at}googlemail.com


  Abstract

We present the status of the Farrell–Jones Conjecture for algebraic K-theory for a group G and arbitrary coefficient rings R. We add new groups for which the conjecture is known to be true, and we study inheritance properties. We discuss new applications, focussing on the Bass Conjecture, the Kaplansky Conjecture, and conjectures generalizing Moody's Induction Theorem. Thus, we considerably extend the class of groups for which these conjectures are known.

Received April 10, 2007.

2000 Mathematics Subject Classification 19Dxx, 19A31, 19B28


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