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.References
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Additional Information
- Peter Linnell
- Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061-0123
- MR Author ID: 114455
- Email: plinnell@math.vt.edu
- Wolfgang Lück
- Affiliation: Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einstein- strasse 62, D-48149 Münster, Germany
- Email: lueck@math.uni-muenster.de
- Roman Sauer
- Affiliation: Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einstein- strasse 62, D-48149 Münster, Germany
- Email: sauerr@uni-muenster.de
- Received by editor(s): March 1, 2010
- Published electronically: September 21, 2010
- Additional Notes: The authors thank the HIM at Bonn for its hospitality during the trimester program “Rigidity” in the fall of 2009, when this paper was written. This work was financially supported by the Leibniz-Preis of the second author.
- Communicated by: Brooke Shipley
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 421-434
- MSC (2010): Primary 16U20, 55P99
- DOI: https://doi.org/10.1090/S0002-9939-2010-10689-5
- MathSciNet review: 2736326