Hyperbolic groups containing subgroups of type ${\mathcal{F}}_3$ not ${\mathcal{F}}_4$

Abstract

We give examples of hyperbolic groups which contain subgroups that are of type ${\mathcal{F}}_3$ but not of type ${\mathcal{F}}_4$. These groups are obtained by Dehn filling starting from a non-uniform lattice in $\mathrm{PO}(8,1)$ which was previously studied by Italiano, Martelli and Migliorini.

24 pages, 1 figure

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