Journal title
Journal of the American Mathematical Society
DOI
10.1090/jams/936
Issue
2
Volume
33
Last updated
2024-03-24T18:56:10.02+00:00
Page
451-486
Abstract
We show that a 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.
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.
Symplectic ID
1118444
Submitted to ORA
On
Favourite
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Publication type
Journal Article
Publication date
24 Dec 2019