柔性群的 L2$L^2$-Betti 扭曲数

IF 0.8 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2024-04-24 DOI:10.1112/blms.13050

Jan Boschheidgen, Andrei Jaikin-Zapirain

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引用次数: 0

摘要

沃尔夫冈-吕克（Wolfgang Lück）提出了这样一个问题：对于一个给定的群，用一个有限维的复表示扭转有限生成的自由-模的链复数，然后再传递到-完成，对-贝蒂数的影响是否除了因子的缩放之外没有其他影响？这篇文章的目的就是要肯定地回答这个问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Twisted L 2 $L^2$ -Betti numbers for sofic groups

For a given group $G$ , Wolfgang Lück asked whether twisting a chain complex of finitely generated free $C [G]$ -modules with a finite-dimensional complex representation $V$ of $G$ before passing to the $L^{2}$ -completion has no other effect on $L^{2}$ -Betti numbers than a scaling by the factor ${dim}_{C} V$ . The purpose of the article is to answer this question affirmatively provided $G$ is sofic.