Algebraic fibring and L^2-Betti numbers
20.30 SR 2.058
A group is said to algebraically fibre if it maps onto Z with finitely generated kernel. The definition and terminology is motivated by a theorem of Stallings, which states that if G is the fundamental group of a closed 3-manifold M and G algebraically fibres, then M fibres over the circle. In 2020, Dawid Kielak showed that finitely generated RFRS groups virtually fibre if and only if they have vanishing first L^2-Betti number. We present the following generalisation of this result: a RFRS of type FP_n(Q) virtually algebraically fibres with kernel of type FP_n(Q) if and only if b_p^(2)(G) = 0 for p < n+1, as well as a version in positive characteristic.