ℓ2$\ell ^2$‐Betti numbers and coherence of random groups
Authors
Kielak, Dawid
Kropholler, Robert
Wilkes, Gareth
Publication Date
2022-03-17Journal Title
Journal of the London Mathematical Society
ISSN
0024-6107
Publisher
Wiley
Language
en
Type
Article
This Version
AO
VoR
Metadata
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Kielak, D., Kropholler, R., & Wilkes, G. (2022). ℓ2$\ell ^2$‐Betti numbers and coherence of random groups. Journal of the London Mathematical Society https://doi.org/10.1112/jlms.12579
Description
Funder: Clare College, Cambridge
Abstract
Abstract: We study ℓ 2 $\ell ^2$ ‐Betti numbers, coherence and (virtual) fibring of random groups in the few‐relator model. In particular, random groups with negative Euler characteristic are coherent, have ℓ 2 $\ell ^2$ ‐homology concentrated in dimension 1 and embed in a virtually free‐by‐cyclic group with high probability. In the case of Euler characteristic zero, we use Novikov homology to show that a random group is free‐by‐cyclic with positive probability.
Keywords
20F65, RESEARCH ARTICLE, RESEARCH ARTICLES
Sponsorship
DFG (SPP2026)
Identifiers
jlms12579, 2003.06354
External DOI: https://doi.org/10.1112/jlms.12579
This record's URL: https://www.repository.cam.ac.uk/handle/1810/335106
Rights
Licence:
http://creativecommons.org/licenses/by-nc-nd/4.0/
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