Vol. 4, No. 1, 2019
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On the Farrell–Jones conjecture for algebraic $K\mkern-2mu$-theory of spaces: the Farrell–Hsiang method

Mark Ullmann and Christoph Winges
Vol. 4 (2019), No. 1, 57–138
DOI: 10.2140/akt.2019.4.57
Abstract

We prove the Farrell–Jones conjecture for algebraic K-theory of spaces for virtually poly-ℤ-groups. For this, we transfer the “Farrell–Hsiang method” from the linear case to categories of equivariant, controlled retractive spaces.

Keywords
algebraic $K\mkern-2mu$-theory of spaces, Farrell–Jones conjecture, poly-$\mathbb Z$-groups
Mathematical Subject Classification 2010
Primary: 19D10
Secondary: 18F25, 57Q10
Milestones
Received: 4 October 2017
Revised: 10 September 2018
Accepted: 27 September 2018
Published: 24 March 2019
Authors
Mark Ullmann
Institut für Mathematik
Freie Universität Berlin
Berlin
Germany
Christoph Winges
Mathematisches Institut
Rheinische Friedrich-Wilhelms-Universität
Bonn
Germany