The Farrell–Jones conjecture for normally poly-free groups
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- by Benjamin Brück, Dawid Kielak and Xiaolei Wu
- Proc. Amer. Math. Soc. 149 (2021), 2349-2356
- DOI: https://doi.org/10.1090/proc/15357
- Published electronically: March 23, 2021
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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.References
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Bibliographic 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
- 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: https://doi.org/10.1090/proc/15357
- MathSciNet review: 4246787