The limit of 𝔽_{𝕡}-Betti numbers of a tower of finite covers with amenable fundamental groups

Linnell, Peter; Lück, Wolfgang; Sauer, Roman

doi:10.1090/S0002-9939-2010-10689-5

The limit of $\mathbb {F}_p$-Betti numbers of a tower of finite covers with amenable fundamental groups
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by Peter Linnell, Wolfgang Lück and Roman Sauer PDF

Proc. Amer. Math. Soc. 139 (2011), 421-434 Request permission

Abstract:

We prove an analogue of the Approximation Theorem of $L^2$-Betti numbers by Betti numbers for arbitrary coefficient fields and virtually torsionfree amenable groups. The limit of Betti numbers is identified as the dimension of some module over the Ore localization of the group ring.

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