Kropholler, Robert and Walsh, Genevieve S. (2022) Incoherence and fibering of many free-by-free groups. Annales de l'Institut Fourier, 72 (6). pp. 2385-2397. doi:10.5802/aif.3494 ISSN 1777-5310.

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Abstract

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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Geometric group theory, Fiberings (Mathematics), Group theory
Journal or Publication Title:	Annales de l'Institut Fourier
Publisher:	Association des Annales de l'Institut Fourier
ISSN:	1777-5310
Official Date:	22 October 2022
Dates:	Date Event 22 October 2022 Published 13 November 2020 Accepted
Volume:	72
Number:	6
Page Range:	pp. 2385-2397
DOI:	10.5802/aif.3494
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access (Creative Commons)
Date of first compliant deposit:	22 December 2022
Date of first compliant Open Access:	22 December 2022
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID DMS-1709964 [NSF] National Science Foundation (US) http://dx.doi.org/10.13039/100000001

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