Twisted L2$L^2$‐Betti numbers for sofic groups

Abstract

AbstractFor a given group , Wolfgang Lück asked whether twisting a chain complex of finitely generated free ‐modules with a finite‐dimensional complex representation of before passing to the ‐completion has no other effect on ‐Betti numbers than a scaling by the factor . The purpose of the article is to answer this question affirmatively provided is sofic.