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Residually finite rationally solvable groups and virtual fibring

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arxiv 1809.09386 v2 pith:EIAQC35L submitted 2018-09-25 math.GR math.GT

Dawid Kielak This is my paper · ORCID
classification math.GRmath.GT
keywords finitefinitelygeneratedgroupsrationallyresiduallysolvablevirtual
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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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Cited by 1 Pith paper

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  1. Cubulating Surface-by-free Groups

    math.GT 2019-08 conditional novelty 7.0 of 10

    Surface-by-free hyperbolic groups are cubulable when the monodromy comes from a sufficiently thick tight tree of homologous curves, because the group contains an essential incompressible quasiconvex track.

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