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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The limit of $ \mathbb{F}_p$-Betti numbers of a tower of finite covers with amenable fundamental groups


Authors: Peter Linnell, Wolfgang Lück and Roman Sauer
Journal: Proc. Amer. Math. Soc. 139 (2011), 421-434
MSC (2010): Primary 16U20, 55P99
Published electronically: September 21, 2010
MathSciNet review: 2736326
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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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Peter Linnell
Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061-0123
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

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10689-5
PII: S 0002-9939(2010)10689-5
Keywords: Amenability, Ore localization, Betti numbers
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.