Residually finite rationally solvable groups and virtual fibring

By Dawid Kielak. 2018

69 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9c0ec374679f07315bf63aa42f6711e9a02b2b30