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ℓ 2 $\ell ^2$ ‐Betti numbers and coherence of random groups
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Kielak, Dawid, Kropholler, Robert and Wilkes, Gareth (2022) ℓ 2 $\ell ^2$ ‐Betti numbers and coherence of random groups. Journal of the London Mathematical Society, 106 (1). pp. 425-445. doi:10.1112/jlms.12579 ISSN 0024-6107.
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Official URL: https://doi.org/10.1112/jlms.12579
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.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
SWORD Depositor: | Library Publications Router | ||||||||
Journal or Publication Title: | Journal of the London Mathematical Society | ||||||||
Publisher: | Wiley | ||||||||
ISSN: | 0024-6107 | ||||||||
Official Date: | July 2022 | ||||||||
Dates: |
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Volume: | 106 | ||||||||
Number: | 1 | ||||||||
Page Range: | pp. 425-445 | ||||||||
DOI: | 10.1112/jlms.12579 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Copyright Holders: | © 2022 The Authors. Journal of the London Mathematical Society is copyright © London Mathematical Society. | ||||||||
Date of first compliant deposit: | 18 November 2022 | ||||||||
Date of first compliant Open Access: | 18 November 2022 | ||||||||
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