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arXiv · 1809.09386

Residually finite rationally solvable groups and virtual fibring

Dawid Kielak
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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.

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Dawid Kielak. 2018-09-25. Residually finite rationally solvable groups and virtual fibring. https://doi.org/10.1090/jams/936

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