[L’incohérence et le caractère fibré des extensions d’un groupe libre par un groupe libre]
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 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.
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 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.
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Keywords: incoherence, free-by-free, surface-by-free, algebraic fibering
Mot clés : incohérent, fibrent algébriquement
Kropholler, Robert P. 1 ; Walsh, Genevieve S. 2
CC-BY-ND 4.0
@article{AIF_2022__72_6_2385_0,
author = {Kropholler, Robert P. and Walsh, Genevieve S.},
title = {Incoherence and fibering of many free-by-free groups},
journal = {Annales de l'Institut Fourier},
pages = {2385--2397},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {72},
number = {6},
year = {2022},
doi = {10.5802/aif.3494},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3494/}
}
TY - JOUR AU - Kropholler, Robert P. AU - Walsh, Genevieve S. TI - Incoherence and fibering of many free-by-free groups JO - Annales de l'Institut Fourier PY - 2022 SP - 2385 EP - 2397 VL - 72 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3494/ DO - 10.5802/aif.3494 LA - en ID - AIF_2022__72_6_2385_0 ER -
%0 Journal Article %A Kropholler, Robert P. %A Walsh, Genevieve S. %T Incoherence and fibering of many free-by-free groups %J Annales de l'Institut Fourier %D 2022 %P 2385-2397 %V 72 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3494/ %R 10.5802/aif.3494 %G en %F AIF_2022__72_6_2385_0
Kropholler, Robert P.; Walsh, Genevieve S. Incoherence and fibering of many free-by-free groups. Annales de l'Institut Fourier, Tome 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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