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:
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 81531
Deposited By: ep_importer_pure
Deposited On: 12 Sep 2016 09:36
Refereed?: Yes
Published?: Published
Last Modified: 27 Feb 2020 03:20
URI: https://eprints.lancs.ac.uk/id/eprint/81531

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