Incoherence and fibering of many free-by-free groups
Annales de l'Institut Fourier, Volume 72 (2022) no. 6, pp. 2385-2397.

We show that free-by-free groups satisfying a homological criterion, which we call excessive homology, are incoherent. This class is large in nature, including many examples of hyperbolic and non-hyperbolic free-by-free groups. We apply this criterion to finite index subgroups of F 2 F n to show incoherence of all such groups, and to other similar classes of groups. Furthermore, we show that a large class of groups, including free-by-free, surface-by-surface, and finitely generated-by-RAAG, algebraically fiber if they have excessive homology.

Nous montrons que les extensions d’un groupe libre par un groupe libre satisfaisant un critère homologique, que nous appelons “ homologie excessive ”, sont incohérents. Cette classe est large et comprend de nombreux exemples de groupes hyperboliques et non hyperboliques. Nous appliquons ce critère aux sous-groupes d’indice fini de F 2 F n pour montrer l’incohérence de tous ces groupes, et à d’autres classes de groupes similaires. De plus, nous montrons que les groupes d’une plus vaste classe, incluant les extensions d’un groupe libre par un groupe libre, d’un groupe de surface par un groupe de surface, d’un groupe de type fini par un groupe d’Artin á angles droits, fibrent algébriquement s’ils ont une homologie excessive.

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Accepted:
Published online:
DOI: 10.5802/aif.3494
Classification: 20F65
Keywords: incoherence, free-by-free, surface-by-free, algebraic fibering
Kropholler, Robert P. 1; Walsh, Genevieve S. 2

1 Mathematics Institute Zeeman Building University of Warwick Coventry, England
2 Department of Mathematics Tufts University Medford, MA USA
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Kropholler, Robert P.; Walsh, Genevieve S. Incoherence and fibering of many free-by-free groups. Annales de l'Institut Fourier, Volume 72 (2022) no. 6, pp. 2385-2397. doi : 10.5802/aif.3494. https://aif.centre-mersenne.org/articles/10.5802/aif.3494/

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