Homological growth of Artin kernels in positive characteristic
Homological growth of Artin kernels in positive characteristic
We prove an analogue of the Lück Approximation Theorem in positive characteristic for certain residually finite rationally soluble (RFRS) groups including right-angled Artin groups and Bestvina–Brady groups. Specifically, we prove that the mod p homology growth equals the dimension of the group homology with coefficients in a certain universal division ring and this is independent of the choice of residual chain. For general RFRS groups we obtain an inequality between the invariants. We also consider a number of applications to fibring, amenable category, and minimal volume entropy.
Artin groups, L2 Betti numbers, Luck approximation, homology growth
Leary, Ian
57bd5c53-cd99-41f9-b02a-4a512d45150e
Hughes, Sam
dd73f4ab-388b-4151-8cb3-2ab484590d82
Fisher, Sam
1698d3e8-1ca6-46ad-9c94-cff8b7328999
Leary, Ian
57bd5c53-cd99-41f9-b02a-4a512d45150e
Hughes, Sam
dd73f4ab-388b-4151-8cb3-2ab484590d82
Fisher, Sam
1698d3e8-1ca6-46ad-9c94-cff8b7328999
Leary, Ian, Hughes, Sam and Fisher, Sam
(2023)
Homological growth of Artin kernels in positive characteristic.
Mathematische Annalen.
(doi:10.1007/s00208-023-02663-1).
Abstract
We prove an analogue of the Lück Approximation Theorem in positive characteristic for certain residually finite rationally soluble (RFRS) groups including right-angled Artin groups and Bestvina–Brady groups. Specifically, we prove that the mod p homology growth equals the dimension of the group homology with coefficients in a certain universal division ring and this is independent of the choice of residual chain. For general RFRS groups we obtain an inequality between the invariants. We also consider a number of applications to fibring, amenable category, and minimal volume entropy.
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Accepted/In Press date: 20 June 2023
e-pub ahead of print date: 6 July 2023
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Publisher Copyright:
© 2023, The Author(s).
Keywords:
Artin groups, L2 Betti numbers, Luck approximation, homology growth
Identifiers
Local EPrints ID: 478590
URI: http://eprints.soton.ac.uk/id/eprint/478590
ISSN: 0025-5831
PURE UUID: 86da5bbc-420d-462e-afe4-4180dcb0752e
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Date deposited: 05 Jul 2023 17:15
Last modified: 13 Apr 2024 01:43
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Author:
Sam Hughes
Author:
Sam Fisher
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