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The Farrell–Jones conjecture for normally poly-free groups


Authors: Benjamin Brück, Dawid Kielak and Xiaolei Wu
Journal: Proc. Amer. Math. Soc. 149 (2021), 2349-2356
MSC (2020): Primary 18F25, 19A31, 19B28
DOI: https://doi.org/10.1090/proc/15357
Published electronically: March 23, 2021
MathSciNet review: 4246787
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Abstract: 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: benjamin.brueck@math.ethz.ch

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: kielak@maths.ox.ac.uk

Xiaolei Wu
Affiliation: Universität Bielefeld, Institut für Mathematik, Universitätsstraße 25, 33501 Bielefeld, Germany
MR Author ID: 1071753
ORCID: 0000-0003-2064-4455
Email: xwu@math.uni-bielefeld.de

Keywords: The Farrell–Jones Conjecture, K-theory of group rings, L-theory of group rings, Artin groups, right-angled Artin group, normally poly-free groups
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
Article copyright: © Copyright 2021 American Mathematical Society