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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Residually finite rationally solvable groups and virtual fibring
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by Dawid Kielak HTML | PDF
J. Amer. Math. Soc. 33 (2020), 451-486 Request permission


We show that a non-trivial finitely generated residually finite rationally solvable (or RFRS) group $G$ is virtually fibred, in the sense that it admits a virtual surjection to $\mathbb {Z}$ with a finitely generated kernel, if and only if the first $L^2$-Betti number of $G$ vanishes. This generalises (and gives a new proof of) the analogous result of Ian Agol for fundamental groups of $3$-manifolds.
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Additional Information
  • Dawid Kielak
  • Affiliation: Fakultät für Mathematik, Universität Bielefeld, Postfach 100131 D-33501 Bielefeld, Germany
  • MR Author ID: 1027989
  • ORCID: 0000-0002-5536-9070
  • Email:
  • Received by editor(s): September 25, 2018
  • Received by editor(s) in revised form: July 22, 2019, and August 27, 2019
  • Published electronically: December 24, 2019
  • Additional Notes: The author was supported by the grant KI 1853/3-1 within the Priority Programme 2026 ‘Geometry at Infinity’ of the German Science Foundation (DFG)
  • © Copyright 2019 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 33 (2020), 451-486
  • MSC (2010): Primary 20F65; Secondary 57M10, 20E26, 12E15, 16S35, 20J05
  • DOI:
  • MathSciNet review: 4073866