香蕉视频

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Title: Algebraic fibring and L^2-Betti numbers

Abstract: A celebrated theorem of Stallings states that if G is the fundamental group of a 3-manifold M, then G maps to Z with finitely generated kernel if and only if M fibres over the circle. In light of this theorem, we say that a group G algebraically fibres if it maps to Z with finitely generated kernel. In 2020, Kielak showed that a RFRS group virtually algebraically fibres if and only if its first L^2-Betti number vanishes, generalising Agol's fibring crietrion for 3-manifolds. In this talk, we will present a generalisation of this theorem, which relates the vanishing of the higher L^2-Betti numbers to higher finiteness properties of the kernel in the algebraic fibration. We will also introduce positive characteristic variants of L^2-Betti numbers and use them to present a positive characteristic version of our main theorem.

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