Home > Research > Publications & Outputs > On computing homology gradients over finite fields

Electronic data

  • 1410.1693v3

    Rights statement: 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.

    Accepted author manuscript, 515 KB, PDF document

    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License

Links

Text available via DOI:

Keywords

View graph of relations

On computing homology gradients over finite fields

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>05/2017
<mark>Journal</mark>Mathematical Proceedings of the Cambridge Philosophical Society
Issue number3
Volume162
Number of pages26
Pages (from-to)507-532
Publication StatusPublished
Early online date5/08/16
<mark>Original language</mark>English

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.

Bibliographic note

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.