剩余有限合理可解群与虚纤维

Dawid Kielak
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引用次数: 44

摘要

我们证明了一个有限生成的剩余有限合理可解(或RFRS)群$G$是虚纤维的,即当且仅当$G$的第一个$L^2$-Betti数消失时,它承认具有有限生成核的$\mathbb{Z}$的虚抛射。这推广了Ian Agol关于$3$-流形基本群的类似结果(并给出了一个新的证明)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Residually finite rationally solvable groups and virtual fibring
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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