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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Farrell–Jones conjecture for normally poly-free groups
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by Benjamin Brück, Dawid Kielak and Xiaolei Wu PDF
Proc. Amer. Math. Soc. 149 (2021), 2349-2356 Request permission


We prove the $K$- and $L$-theoretic Farrell–Jones Conjecture with coefficients in an additive category for every normally poly-free group, in particular for even Artin groups of FC-type, and for all groups of the form $A\rtimes \mathbb {Z}$ where $A$ is a right-angled Artin group. Our proof relies on the work of Bestvina–Fujiwara–Wigglesworth on the Farrell–Jones Conjecture for free-by-cyclic groups.
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Additional Information
  • Benjamin Brück
  • Affiliation: ETH Zurich, Department of Mathematics, HG J 43, Rämistrasse 101, 8092 Zurich, Switzerland
  • Email:
  • Dawid Kielak
  • Affiliation: Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, United Kingdom
  • MR Author ID: 1027989
  • ORCID: 0000-0002-5536-9070
  • Email:
  • Xiaolei Wu
  • Affiliation: Universität Bielefeld, Institut für Mathematik, Universitätsstraße 25, 33501 Bielefeld, Germany
  • MR Author ID: 1071753
  • ORCID: 0000-0003-2064-4455
  • Email:
  • Received by editor(s): September 24, 2019
  • Received by editor(s) in revised form: September 21, 2020
  • Published electronically: March 23, 2021
  • Additional Notes: The first and second authors were supported by grants BU 1224/2-1 and KI 1853/3-1, respectively, within the Priority Programme 2026 “Geometry at infinity” of the German Science Foundation (DFG)
    The third author was partially supported by Wolfgang Lück’s ERC Advanced Grant “KL2MG-interactions” (no. 662400) and the DFG Grant under Germany’s Excellence Strategy - GZ 2047/1, Projekt-ID 390685813.
  • Communicated by: Kenneth Bromberg
  • © Copyright 2021 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 149 (2021), 2349-2356
  • MSC (2020): Primary 18F25, 19A31, 19B28
  • DOI:
  • MathSciNet review: 4246787