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arXiv · 1910.09601

Incoherence and fibering of many free-by-free groups

Robert Kropholler·Genevieve Walsh
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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 $F_2\rtimes F_n$ 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.

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Robert Kropholler, Genevieve Walsh. 2019-10-21. Incoherence and fibering of many free-by-free groups. https://arxiv.org/abs/1910.09601

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