On computing homology gradients over finite fields

Grabowski, Łukasz and Schick, Thomas (2017) On computing homology gradients over finite fields. Mathematical Proceedings of the Cambridge Philosophical Society, 162 (3). pp. 507-532. ISSN 0305-0041

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Abstract

Recently the so-called Atiyah conjecture about l^2-Betti numbers has been disproved. The counterexamples were found using a specific method of computing the spectral measure of a matrix over a complex group ring. We show that in many situations the same method allows to compute homology gradients, i.e. generalizations of l^2-Betti numbers to fields of arbitrary characteristic. As an application we point out that (i) the homology gradient over any field of characteristic different than 2 can be an irrational number, and (ii) there exists a finite CW-complex with the property that the homology gradients of its universal cover taken over different fields have infinitely many different values.

Item Type:
Journal Article
Journal or Publication Title:
Mathematical Proceedings of the Cambridge Philosophical Society
Additional Information:
https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society The final, definitive version of this article has been published in the Journal, Mathematical Proceedings of the Cambridge Philosophical Society, 162 (3), pp 507-532 2017, © 2016 Cambridge University Press.
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
81531
Deposited By:
Deposited On:
12 Sep 2016 09:36
Refereed?:
Yes
Published?:
Published
Last Modified:
06 Aug 2020 03:49