剩余有限合理可解群与虚纤维

arXiv: Group Theory Pub Date : 2018-09-25 DOI:10.1090/jams/936

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)。

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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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arXiv: Group Theory

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